# bibtab

bibtype: article
filename: elefunt.bib
label: Linhart:2009:ACL
author: Jean Marie Linhart
title: Algorithm 885: Computing the Logarithm of the Normal Distribution
journal: j-TOMS
volume: 35
number: 3
pages: 20:1--20:10
month: oct
monthnumber: 10
year: 2009
CODEN: ACMSCU
DOI: https://doi.org/10.1145/1391989.1391993
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Sat Nov 1 19:57:00 MDT 2008
bibtimestamp: 2008.11.01 19:57:00 MDT
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: error function; logarithm of the standard normal distribution; Normal distribution; normal integral
acknowledgement: ack-nhfb
articleno: 20
journalURL: https://dl.acm.org/loi/toms
rawauthor: Jean Marie Linhart
rawtitle: {Algorithm 885}: Computing the Logarithm of the Normal Distribution
abstract:
We present and compare three C functions to compute the logarithm of the cumulative standard normal distribution. The first is a new algorithm derived from Algorithm 304's calculation of the standard normal distribution via a series or continued fraction approximation, and it is good to the accuracy of the machine. The second is based on Algorithm 715's calculation of the standard normal distribution via rational Chebyshev approximation. This is related to, and an improvement on, the algorithm for the logarithm of the normal distribution available in the software package R. The third is a new and simple algorithm that uses the compiler's implementation of the error function, and complement of the error function, to compute the log of the normal distribution.

rawabstract:
We present and compare three C functions to compute the logarithm of the cumulative standard normal distribution. The first is a new algorithm derived from Algorithm 304's calculation of the standard normal distribution via a series or continued fraction approximation, and it is good to the accuracy of the machine. The second is based on Algorithm 715's calculation of the standard normal distribution via rational Chebyshev approximation. This is related to, and an improvement on, the algorithm for the logarithm of the normal distribution available in the software package R. The third is a new and simple algorithm that uses the compiler's implementation of the error function, and complement of the error function, to compute the log of the normal distribution.

entry:
@Article{Linhart:2009:ACL,
  author =       "Jean Marie Linhart",
  title =        "{Algorithm 885}: Computing the Logarithm of the Normal
                 Distribution",
  journal =      j-TOMS,
  volume =       "35",
  number =       "3",
  pages =        "20:1--20:10",
  month =        oct,
  year =         "2009",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1391989.1391993",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 1 19:57:00 MDT 2008",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We present and compare three C functions to compute
                 the logarithm of the cumulative standard normal
                 distribution. The first is a new algorithm derived from
                 Algorithm 304's calculation of the standard normal
                 distribution via a series or continued fraction
                 approximation, and it is good to the accuracy of the
                 machine. The second is based on Algorithm 715's
                 calculation of the standard normal distribution via
                 rational Chebyshev approximation. This is related to,
                 and an improvement on, the algorithm for the logarithm
                 of the normal distribution available in the software
                 package R. The third is a new and simple algorithm that
                 uses the compiler's implementation of the error
                 function, and complement of the error function, to
                 compute the log of the normal distribution.",
  acknowledgement = ack-nhfb,
  articleno =    "20",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "error function; logarithm of the standard normal
                 distribution; Normal distribution; normal integral",
}


bibtype: article
filename: elefunt.bib
label: Loskot:2009:PPA
author: P. Loskot and N. C. Beaulieu
journal: j-IEEE-TRANS-VEH-TECHNOL
volume: 58
number: 3
pages: 1269--1280
month: mar
monthnumber: 3
year: 2009
CODEN: ITUTAB
DOI: https://doi.org/10.1109/tvt.2008.926072
ISSN: 0018-9545 (print), 1939-9359 (electronic) OR 00189545 (print), 19399359 (electronic)
ISSNL: 0018-9545 OR 00189545
bibdate: Sat Dec 16 18:08:41 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.12.16 18:08:41 ???
URL: http://ieeexplore.ieee.org/document/4529094/
fjournal: IEEE Transactions on Vehicular Technology
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=25
rawauthor: P. Loskot and N. C. Beaulieu
title:
Prony and Polynomial Approximations for Evaluation of the Average Probability of Error Over Slow-Fading Channels

rawtitle:
{Prony} and Polynomial Approximations for Evaluation of the Average Probability of Error Over Slow-Fading Channels

entry:
@Article{Loskot:2009:PPA,
  author =       "P. Loskot and N. C. Beaulieu",
  title =        "{Prony} and Polynomial Approximations for Evaluation
                 of the Average Probability of Error Over Slow-Fading
                 Channels",
  journal =      j-IEEE-TRANS-VEH-TECHNOL,
  volume =       "58",
  number =       "3",
  pages =        "1269--1280",
  month =        mar,
  year =         "2009",
  CODEN =        "ITUTAB",
  DOI =          "https://doi.org/10.1109/tvt.2008.926072",
  ISSN =         "0018-9545 (print), 1939-9359 (electronic)",
  ISSN-L =       "0018-9545",
  bibdate =      "Sat Dec 16 18:08:41 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://ieeexplore.ieee.org/document/4529094/",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Vehicular Technology",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=25",
}


bibtype: article
filename: elefunt.bib
label: Nagayama:2009:CGB
author: S. Nagayama and T. Sasao
title: Complexities of Graph-Based Representations for Elementary Functions
journal: j-IEEE-TRANS-COMPUT
volume: 58
number: 1
pages: 106--119
month: jan
monthnumber: 1
year: 2009
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.2008.134
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Mon Jul 4 11:37:39 MDT 2011
bibtimestamp: 2011.07.04 11:37:39 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4599569
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: S. Nagayama and T. Sasao
rawtitle: Complexities of Graph-Based Representations for Elementary Functions
abstract:
This paper analyzes complexities of decision diagrams for elementary functions such as polynomial, trigonometric, logarithmic, square root, and reciprocal functions. These real functions are converted into integer-valued functions by using fixed-point representation. This paper presents the numbers of nodes in decision diagrams representing the integer-valued functions. First, complexities of decision diagrams for polynomial functions are analyzed, since elementary functions can be approximated by polynomial functions. A theoretical analysis shows that binary moment diagrams (BMDs) have low complexity for polynomial functions. Second, this paper analyzes complexity of edge-valued binary decision diagrams (EVBDDs) for monotone functions, since many common elementary functions are monotone. It introduces a new class of integer functions, Mp-monotone increasing function, and derives an upper bound on the number of nodes in an EVBDD for the Mp-monotone increasing function. A theoretical analysis shows that EVBDDs have low complexity for Mp-monotone increasing functions. This paper also presents the exact number of nodes in the smallest EVBDD for the n-bit multiplier function, and a variable order for the smallest EVBDD.

keywords:
binary moment diagram; decision diagrams; edge-valued binary decision diagram; elementary function; elementary function approximation; fixed-point representation; general representations; graph-based representation; integer-valued function; monotone function; polynomial function; trees

rawabstract:
This paper analyzes complexities of decision diagrams for elementary functions such as polynomial, trigonometric, logarithmic, square root, and reciprocal functions. These real functions are converted into integer-valued functions by using fixed-point representation. This paper presents the numbers of nodes in decision diagrams representing the integer-valued functions. First, complexities of decision diagrams for polynomial functions are analyzed, since elementary functions can be approximated by polynomial functions. A theoretical analysis shows that binary moment diagrams (BMDs) have low complexity for polynomial functions. Second, this paper analyzes complexity of edge-valued binary decision diagrams (EVBDDs) for monotone functions, since many common elementary functions are monotone. It introduces a new class of integer functions, Mp-monotone increasing function, and derives an upper bound on the number of nodes in an EVBDD for the Mp-monotone increasing function. A theoretical analysis shows that EVBDDs have low complexity for Mp-monotone increasing functions. This paper also presents the exact number of nodes in the smallest EVBDD for the n-bit multiplier function, and a variable order for the smallest EVBDD.

entry:
@Article{Nagayama:2009:CGB,
  author =       "S. Nagayama and T. Sasao",
  title =        "Complexities of Graph-Based Representations for
                 Elementary Functions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "58",
  number =       "1",
  pages =        "106--119",
  month =        jan,
  year =         "2009",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2008.134",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 11:37:39 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4599569",
  abstract =     "This paper analyzes complexities of decision diagrams
                 for elementary functions such as polynomial,
                 trigonometric, logarithmic, square root, and reciprocal
                 functions. These real functions are converted into
                 integer-valued functions by using fixed-point
                 representation. This paper presents the numbers of
                 nodes in decision diagrams representing the
                 integer-valued functions. First, complexities of
                 decision diagrams for polynomial functions are
                 analyzed, since elementary functions can be
                 approximated by polynomial functions. A theoretical
                 analysis shows that binary moment diagrams (BMDs) have
                 low complexity for polynomial functions. Second, this
                 paper analyzes complexity of edge-valued binary
                 decision diagrams (EVBDDs) for monotone functions,
                 since many common elementary functions are monotone. It
                 introduces a new class of integer functions,
                 Mp-monotone increasing function, and derives an upper
                 bound on the number of nodes in an EVBDD for the
                 Mp-monotone increasing function. A theoretical analysis
                 shows that EVBDDs have low complexity for Mp-monotone
                 increasing functions. This paper also presents the
                 exact number of nodes in the smallest EVBDD for the
                 n-bit multiplier function, and a variable order for the
                 smallest EVBDD.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "binary moment diagram; decision diagrams; edge-valued
                 binary decision diagram; elementary function;
                 elementary function approximation; fixed-point
                 representation; general representations; graph-based
                 representation; integer-valued function; monotone
                 function; polynomial function; trees",
}


bibtype: book
filename: elefunt.bib
label: Oldham:2009:AF
editor: Keith B. Oldham and Jan Myland and Jerome Spanier
title: An Atlas of Functions: With Equator, the Atlas Function Calculator
publisher: pub-SV
address: pub-SV:adr
edition: Second
pages: xi + 748
year: 2009
DOI: https://doi.org/10.1007/978-0-387-48807-3
LCCN: QA331 .S685 2009
bibdate: Fri Aug 31 16:20:13 MDT 2007
bibtimestamp: 2007.08.31 16:20:13 MDT
subject: Functions
acknowledgement: ack-nhfb
raweditor: Keith B. Oldham and Jan Myland and Jerome Spanier
rawtitle: An Atlas of Functions: With Equator, the Atlas Function Calculator
ISBN:
0-387-48807-3 (softcover), 0-387-48806-5 (hardcover) OR 0387488073 (softcover), 0387488065 (hardcover)

ISBN13:
978-0-387-48807-3 (softcover), 978-0-387-48806-6 (hardcover) OR 9780387488073 (softcover), 9780387488066 (hardcover)

bibsource:
https://www.math.utah.edu/pub/tex/bib/canjstat.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager

TOC:
Front Matter / i--xi General Considerations / 1--11 The Constant Function $c$ / 13--19 The Factorial Function $n!$ / 21--27 The Zeta Numbers and Related Functions / 29--38 The Bernoulli Numbers $B_n$ / 39--44 The Euler Numbers $E_n$ / 45--48 The Binomial Coefficients $binom nu m$ / 49--56 The Linear Function $b x + c$ and Its Reciprocal / 57--65 Modifying Functions / 67--74 The Heaviside $u(x - a)$ And Dirac $delta (x - a)$ Functions / 75--80 The Integer Powers $x^n$ and $(b x + c)^n$ / 81--93 The Square-Root Function $sqrt b x + c$ and Its Reciprocal / 95--102 The Noninteger Powers $x^nu $ / 103--112 The Semielliptic Function $(b / a)sqrt a^2 - x^2$ and Its Reciprocal / 113--120 The Semihyperbolic Functions $(b / a) sqrt x^2 pm a^2$ and Their Reciprocals / 121--130 The Quadratic Function $a x^2 + b x + c$ and Its Reciprocal / 131--138 The Cubic Function $x^3 + a x^2 + b x + c$ / 139--146 Polynomial Functions / 147--158 The Pochhammer Polynomials $(x)_n$ / 159--174 The Bernoulli Polynomials $B_n(x)$ / 175--180 The Euler Polynomials $E_n(x)$ / 181--186 The Legendre Polynomials $P_n(x)$ / 187--196 The Chebyshev Polynomials $T_n(x)$ and $U_n(x)$ / 197--208 The Laguerre Polynomials $L_n(x)$ / 209--216 The Hermite Polynomials $H_n(x)$ / 217--227 The Logarithmic Function $ln (x)$ / 229--239 The Exponential Function $exp (pm x)$ / 241--253 Exponentials of Powers $exp (pm x^nu )$ / 255--267 The Hyperbolic Cosine $cosh (x)$ and Sine $sinh (x)$ Functions / 269--279 The Hyperbolic Secant $sech (x)$ and Cosecant $csch (x)$ Functions / 281--288 The Hyperbolic Tangent $tanh (x)$ and Cotangent $coth (x)$ Functions / 289--296 The Inverse Hyperbolic Functions / 297--307 The Cosine $cos (x)$ and Sine $sin (x)$ Functions / 309--328 The Secant $sec (x)$ and Cosecant $csc (x)$ Functions / 329--338 The Tangent $tan (x)$ and Cotangent $cot (x)$ Functions / 339--350 The Inverse Circular Functions / 351--366 Periodic Functions / 367--374 The Exponential Integrals $Ei (x)$ and $Ein (x)$ / 375--383 Sine and Cosine Integrals / 385--394 The Fresnel Integrals $C(x)$ and $S(x)$ / 395--404 The Error Function $erf (x)$ and Its Complement $erfc (x)$ / 405--415 The $exp (x)erfc (sqrt x)$ and Related Functions / 417--426 Dawson's Integral $daw (x)$ / 427--433 The Gamma Function $Gamma (nu )$ / 435--448 The Digamma Function $psi (nu )$ / 449--460 The Incomplete Gamma Functions / 461--470 The Parabolic Cylinder Function $D_nu (x)$ / 471--484 The Kummer Function $M(a, c, x)$ / 485--496 The Tricomi Function $U(a, c, x)$ / 497--506 The Modified Bessel Functions $I_n(x)$ of Integer Order / 507--517 The Modified Bessel Function $I_nu (x)$ of Arbitrary Order / 519--526 The Macdonald Function $K_nu (x)$ / 527--536 The Bessel Functions $J_n(x)$ of Integer Order / 537--552 The Bessel Function $J_nu (x)$ of Arbitrary Order / 553--565 The Neumann Function $Y_nu (x)$ / 567--576 The Kelvin Functions / 577--584 The Airy Functions $Ai (x)$ and $Bi (x)$ / 585--592 The Struve Function $h_nu (x)$ / 593--601 The Incomplete Beta Function $B(nu , mu , x)$ / 603--609 The Legendre Functions $P_nu (x)$ and $Q_nu (x)$ / 611--626 The Gauss Hypergeometric Function $F(a, b, c, x)$ / 627--636 The Complete Elliptic Integrals $K(k)$ and $E(k)$ / 637--651 The Incomplete Elliptic Integrals $F(k, phi )$ and $E(k, phi )$ / 653--669 The Jacobian Elliptic Functions / 671--684 The Hurwitz Function $zeta (nu , u)$ / 685--695 Back Matter / 697--748

rawTOC:
Front Matter / i--xi \\ General Considerations / 1--11 \\ The Constant Function $c$ / 13--19 \\ The Factorial Function $n!$ / 21--27 \\ The Zeta Numbers and Related Functions / 29--38 \\ The Bernoulli Numbers $B_n$ / 39--44 \\ The Euler Numbers $E_n$ / 45--48 \\ The Binomial Coefficients $\binom{\nu}{m}$ / 49--56 \\ The Linear Function $b x + c$ and Its Reciprocal / 57--65 \\ Modifying Functions / 67--74 \\ The Heaviside $u(x - a)$ And Dirac $\delta(x - a)$ Functions / 75--80 \\ The Integer Powers $x^n$ and $(b x + c)^n$ / 81--93 \\ The Square-Root Function $\sqrt{b x + c}$ and Its Reciprocal / 95--102 \\ The Noninteger Powers $x^\nu$ / 103--112 \\ The Semielliptic Function $(b / a)\sqrt{a^2 - x^2}$ and Its Reciprocal / 113--120 \\ The Semihyperbolic Functions $(b / a) \sqrt{x^2 \pm a^2}$ and Their Reciprocals / 121--130 \\ The Quadratic Function $a x^2 + b x + c$ and Its Reciprocal / 131--138 \\ The Cubic Function $x^3 + a x^2 + b x + c$ / 139--146 \\ Polynomial Functions / 147--158 \\ The Pochhammer Polynomials $(x)_n$ / 159--174 \\ The Bernoulli Polynomials $B_n(x)$ / 175--180 \\ The Euler Polynomials $E_n(x)$ / 181--186 \\ The Legendre Polynomials $P_n(x)$ / 187--196 \\ The Chebyshev Polynomials $T_n(x)$ and $U_n(x)$ / 197--208 \\ The Laguerre Polynomials $L_n(x)$ / 209--216 \\ The Hermite Polynomials $H_n(x)$ / 217--227 \\ The Logarithmic Function $\ln(x)$ / 229--239 \\ The Exponential Function $\exp(\pm x)$ / 241--253 \\ Exponentials of Powers $\exp(\pm x^\nu)$ / 255--267 \\ The Hyperbolic Cosine $\cosh(x)$ and Sine $\sinh(x)$ Functions / 269--279 \\ The Hyperbolic Secant $\sech(x)$ and Cosecant $\csch(x)$ Functions / 281--288 \\ The Hyperbolic Tangent $\tanh(x)$ and Cotangent $\coth(x)$ Functions / 289--296 \\ The Inverse Hyperbolic Functions / 297--307 \\ The Cosine $\cos(x)$ and Sine $\sin(x)$ Functions / 309--328 \\ The Secant $\sec(x)$ and Cosecant $\csc(x)$ Functions / 329--338 \\ The Tangent $\tan(x)$ and Cotangent $\cot(x)$ Functions / 339--350 \\ The Inverse Circular Functions / 351--366 \\ Periodic Functions / 367--374 \\ The Exponential Integrals $\Ei(x)$ and $\Ein(x)$ / 375--383 \\ Sine and Cosine Integrals / 385--394 \\ The Fresnel Integrals $C(x)$ and $S(x)$ / 395--404 \\ The Error Function $\erf(x)$ and Its Complement $\erfc(x)$ / 405--415 \\ The $\exp(x)\erfc(\sqrt{x})$ and Related Functions / 417--426 \\ Dawson's Integral $\daw(x)$ / 427--433 \\ The Gamma Function $\Gamma(\nu)$ / 435--448 \\ The Digamma Function $\psi(\nu)$ / 449--460 \\ The Incomplete Gamma Functions / 461--470 \\ The Parabolic Cylinder Function $D_\nu(x)$ / 471--484 \\ The Kummer Function $M(a, c, x)$ / 485--496 \\ The Tricomi Function $U(a, c, x)$ / 497--506 \\ The Modified Bessel Functions $I_n(x)$ of Integer Order / 507--517 \\ The Modified Bessel Function $I_\nu(x)$ of Arbitrary Order / 519--526 \\ The Macdonald Function $K_\nu(x)$ / 527--536 \\ The Bessel Functions $J_n(x)$ of Integer Order / 537--552 \\ The Bessel Function $J_\nu(x)$ of Arbitrary Order / 553--565 \\ The Neumann Function $Y_\nu(x)$ / 567--576 \\ The Kelvin Functions / 577--584 \\ The Airy Functions $\Ai(x)$ and $\Bi(x)$ / 585--592 \\ The Struve Function $h_\nu(x)$ / 593--601 \\ The Incomplete Beta Function $B(\nu, \mu, x)$ / 603--609 \\ The Legendre Functions $P_\nu(x)$ and $Q_\nu(x)$ / 611--626 \\ The Gauss Hypergeometric Function $F(a, b, c, x)$ / 627--636 \\ The Complete Elliptic Integrals $K(k)$ and $E(k)$ / 637--651 \\ The Incomplete Elliptic Integrals $F(k, \phi)$ and $E(k, \phi)$ / 653--669 \\ The Jacobian Elliptic Functions / 671--684 \\ The Hurwitz Function $\zeta(\nu, u)$ / 685--695 \\ Back Matter / 697--748

entry:
@Book{Oldham:2009:AF,
  editor =       "Keith B. Oldham and Jan Myland and Jerome Spanier",
  title =        "An Atlas of Functions: With Equator, the Atlas
                 Function Calculator",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  edition =      "Second",
  pages =        "xi + 748",
  year =         "2009",
  DOI =          "https://doi.org/10.1007/978-0-387-48807-3",
  ISBN =         "0-387-48807-3 (softcover), 0-387-48806-5 (hardcover)",
  ISBN-13 =      "978-0-387-48807-3 (softcover), 978-0-387-48806-6
                 (hardcover)",
  LCCN =         "QA331 .S685 2009",
  bibdate =      "Fri Aug 31 16:20:13 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/canjstat.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  price =        "US\$129.95",
  acknowledgement = ack-nhfb,
  subject =      "Functions",
  tableofcontents = "Front Matter / i--xi \\
                 General Considerations / 1--11 \\
                 The Constant Function $c$ / 13--19 \\
                 The Factorial Function $n!$ / 21--27 \\
                 The Zeta Numbers and Related Functions / 29--38 \\
                 The Bernoulli Numbers $B_n$ / 39--44 \\
                 The Euler Numbers $E_n$ / 45--48 \\
                 The Binomial Coefficients $\binom{\nu}{m}$ / 49--56 \\
                 The Linear Function $b x + c$ and Its Reciprocal /
                 57--65 \\
                 Modifying Functions / 67--74 \\
                 The Heaviside $u(x - a)$ And Dirac $\delta(x - a)$
                 Functions / 75--80 \\
                 The Integer Powers $x^n$ and $(b x + c)^n$ / 81--93 \\
                 The Square-Root Function $\sqrt{b x + c}$ and Its
                 Reciprocal / 95--102 \\
                 The Noninteger Powers $x^\nu$ / 103--112 \\
                 The Semielliptic Function $(b / a)\sqrt{a^2 - x^2}$ and
                 Its Reciprocal / 113--120 \\
                 The Semihyperbolic Functions $(b / a) \sqrt{x^2 \pm
                 a^2}$ and Their Reciprocals / 121--130 \\
                 The Quadratic Function $a x^2 + b x + c$ and Its
                 Reciprocal / 131--138 \\
                 The Cubic Function $x^3 + a x^2 + b x + c$ / 139--146
                 \\
                 Polynomial Functions / 147--158 \\
                 The Pochhammer Polynomials $(x)_n$ / 159--174 \\
                 The Bernoulli Polynomials $B_n(x)$ / 175--180 \\
                 The Euler Polynomials $E_n(x)$ / 181--186 \\
                 The Legendre Polynomials $P_n(x)$ / 187--196 \\
                 The Chebyshev Polynomials $T_n(x)$ and $U_n(x)$ /
                 197--208 \\
                 The Laguerre Polynomials $L_n(x)$ / 209--216 \\
                 The Hermite Polynomials $H_n(x)$ / 217--227 \\
                 The Logarithmic Function $\ln(x)$ / 229--239 \\
                 The Exponential Function $\exp(\pm x)$ / 241--253 \\
                 Exponentials of Powers $\exp(\pm x^\nu)$ / 255--267 \\
                 The Hyperbolic Cosine $\cosh(x)$ and Sine $\sinh(x)$
                 Functions / 269--279 \\
                 The Hyperbolic Secant $\sech(x)$ and Cosecant
                 $\csch(x)$ Functions / 281--288 \\
                 The Hyperbolic Tangent $\tanh(x)$ and Cotangent
                 $\coth(x)$ Functions / 289--296 \\
                 The Inverse Hyperbolic Functions / 297--307 \\
                 The Cosine $\cos(x)$ and Sine $\sin(x)$ Functions /
                 309--328 \\
                 The Secant $\sec(x)$ and Cosecant $\csc(x)$ Functions /
                 329--338 \\
                 The Tangent $\tan(x)$ and Cotangent $\cot(x)$ Functions
                 / 339--350 \\
                 The Inverse Circular Functions / 351--366 \\
                 Periodic Functions / 367--374 \\
                 The Exponential Integrals $\Ei(x)$ and $\Ein(x)$ /
                 375--383 \\
                 Sine and Cosine Integrals / 385--394 \\
                 The Fresnel Integrals $C(x)$ and $S(x)$ / 395--404 \\
                 The Error Function $\erf(x)$ and Its Complement
                 $\erfc(x)$ / 405--415 \\
                 The $\exp(x)\erfc(\sqrt{x})$ and Related Functions /
                 417--426 \\
                 Dawson's Integral $\daw(x)$ / 427--433 \\
                 The Gamma Function $\Gamma(\nu)$ / 435--448 \\
                 The Digamma Function $\psi(\nu)$ / 449--460 \\
                 The Incomplete Gamma Functions / 461--470 \\
                 The Parabolic Cylinder Function $D_\nu(x)$ / 471--484
                 \\
                 The Kummer Function $M(a, c, x)$ / 485--496 \\
                 The Tricomi Function $U(a, c, x)$ / 497--506 \\
                 The Modified Bessel Functions $I_n(x)$ of Integer Order
                 / 507--517 \\
                 The Modified Bessel Function $I_\nu(x)$ of Arbitrary
                 Order / 519--526 \\
                 The Macdonald Function $K_\nu(x)$ / 527--536 \\
                 The Bessel Functions $J_n(x)$ of Integer Order /
                 537--552 \\
                 The Bessel Function $J_\nu(x)$ of Arbitrary Order /
                 553--565 \\
                 The Neumann Function $Y_\nu(x)$ / 567--576 \\
                 The Kelvin Functions / 577--584 \\
                 The Airy Functions $\Ai(x)$ and $\Bi(x)$ / 585--592 \\
                 The Struve Function $h_\nu(x)$ / 593--601 \\
                 The Incomplete Beta Function $B(\nu, \mu, x)$ /
                 603--609 \\
                 The Legendre Functions $P_\nu(x)$ and $Q_\nu(x)$ /
                 611--626 \\
                 The Gauss Hypergeometric Function $F(a, b, c, x)$ /
                 627--636 \\
                 The Complete Elliptic Integrals $K(k)$ and $E(k)$ /
                 637--651 \\
                 The Incomplete Elliptic Integrals $F(k, \phi)$ and
                 $E(k, \phi)$ / 653--669 \\
                 The Jacobian Elliptic Functions / 671--684 \\
                 The Hurwitz Function $\zeta(\nu, u)$ / 685--695 \\
                 Back Matter / 697--748",
}


bibtype: article
filename: elefunt.bib
label: Opps:2009:RFA
author: Sheldon B. Opps and Nasser Saad and H. M. Srivastava
journal: j-APPL-MATH-COMP
volume: 207
number: 2
pages: 545--558
day: 15
month: jan
monthnumber: 1
year: 2009
CODEN: AMHCBQ
ISSN: 0096-3003 (print), 1873-5649 (electronic) OR 00963003 (print), 18735649 (electronic)
ISSNL: 0096-3003 OR 00963003
bibdate: Fri Sep 3 10:53:24 MDT 2010
bibtimestamp: 2010.09.03 10:53:24 MDT
fjournal: Applied Mathematics and Computation
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00963003
rawauthor: Sheldon B. Opps and Nasser Saad and H. M. Srivastava
title:
Recursion formulas for Appell's hypergeometric function $ F_2 $ with some applications to radiation field problems

bibsource:
http://www.sciencedirect.com/science/journal/00963003; https://www.math.utah.edu/pub/tex/bib/applmathcomput2005.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

rawtitle:
Recursion formulas for {Appell}'s hypergeometric function {$ F_2 $} with some applications to radiation field problems

entry:
@Article{Opps:2009:RFA,
  author =       "Sheldon B. Opps and Nasser Saad and H. M. Srivastava",
  title =        "Recursion formulas for {Appell}'s hypergeometric
                 function {$ F_2 $} with some applications to radiation
                 field problems",
  journal =      j-APPL-MATH-COMP,
  volume =       "207",
  number =       "2",
  pages =        "545--558",
  day =          "15",
  month =        jan,
  year =         "2009",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Fri Sep 3 10:53:24 MDT 2010",
  bibsource =    "http://www.sciencedirect.com/science/journal/00963003;
                 https://www.math.utah.edu/pub/tex/bib/applmathcomput2005.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
}


bibtype: article
filename: elefunt.bib
label: Paris:2009:HPE
author: R. B. Paris
title: High-precision evaluation of the Bessel functions via Hadamard series
journal: j-J-COMPUT-APPL-MATH
volume: 224
number: 1
pages: 84--100
day: 1
month: feb
monthnumber: 2
year: 2009
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 13:13:29 MST 2017
bibtimestamp: 2017.02.25 13:13:29 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042708001799
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: R. B. Paris
rawtitle: High-precision evaluation of the {Bessel} functions via {Hadamard} series
entry:
@Article{Paris:2009:HPE,
  author =       "R. B. Paris",
  title =        "High-precision evaluation of the {Bessel} functions
                 via {Hadamard} series",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "224",
  number =       "1",
  pages =        "84--100",
  day =          "1",
  month =        feb,
  year =         "2009",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 13:13:29 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2005.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042708001799",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: mastersthesis
filename: elefunt.bib
label: Pearson:2009:CHF
author: J. Pearson
title: Computation of hypergeometric functions
type: Master's thesis
school: Oxford University
address: Oxford, UK
pages: 84--100
year: 2009
bibdate: Thu Dec 01 09:05:26 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2011.12.01 09:05:26 ???
acknowledgement: ack-nhfb
rawauthor: J. Pearson
rawtitle: Computation of hypergeometric functions
entry:
@MastersThesis{Pearson:2009:CHF,
  author =       "J. Pearson",
  title =        "Computation of hypergeometric functions",
  type =         "{Master}'s thesis",
  school =       "Oxford University",
  address =      "Oxford, UK",
  year =         "2009",
  bibdate =      "Thu Dec 01 09:05:26 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Talman:2009:NSC
author: J. D. Talman
title: NumSBT: a subroutine for calculating spherical Bessel transforms numerically
journal: j-COMP-PHYS-COMM
volume: 180
number: 2
pages: 332--338
month: feb
monthnumber: 2
year: 2009
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/j.cpc.2008.10.003
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Mon Feb 13 23:42:39 MST 2012
bibtimestamp: 2012.02.13 23:42:39 MST
URL: http://www.sciencedirect.com/science/article/pii/S0010465508003329
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: J. D. Talman
rawtitle: {NumSBT}: a subroutine for calculating spherical {Bessel} transforms numerically
entry:
@Article{Talman:2009:NSC,
  author =       "J. D. Talman",
  title =        "{NumSBT}: a subroutine for calculating spherical
                 {Bessel} transforms numerically",
  journal =      j-COMP-PHYS-COMM,
  volume =       "180",
  number =       "2",
  pages =        "332--338",
  month =        feb,
  year =         "2009",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/j.cpc.2008.10.003",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Feb 13 23:42:39 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465508003329",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}


bibtype: article
filename: elefunt.bib
label: Temme:2009:AER
author: Nico M. Temme and Vladimir Varlamov
title: Asymptotic expansions for Riesz fractional derivatives of Airy functions and applications
journal: j-J-COMPUT-APPL-MATH
volume: 232
number: 2
pages: 201--215
day: 15
month: oct
monthnumber: 10
year: 2009
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 13:24:17 MST 2017
bibtimestamp: 2017.02.25 13:24:17 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042709003410
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Nico M. Temme and Vladimir Varlamov
rawtitle: Asymptotic expansions for {Riesz} fractional derivatives of {Airy} functions and applications
entry:
@Article{Temme:2009:AER,
  author =       "Nico M. Temme and Vladimir Varlamov",
  title =        "Asymptotic expansions for {Riesz} fractional
                 derivatives of {Airy} functions and applications",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "232",
  number =       "2",
  pages =        "201--215",
  day =          "15",
  month =        oct,
  year =         "2009",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 13:24:17 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2005.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042709003410",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: inproceedings
filename: elefunt.bib
label: Vazquez:2009:CDT
author: Alvaro Vazquez and Julio Villalba and Elisardo Antelo
title: Computation of Decimal Transcendental Functions Using the CORDIC Algorithm
crossref: Bruguera:2009:PIS
pages: 179--186
year: 2009
bibdate: Fri Jun 12 12:34:25 2009
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2009.06.12 12:34:25 ???
keywords: ARITH-19
acknowledgement: ack-nhfb
rawauthor: {\'A}lvaro V{\'a}zquez and Julio Villalba and Elisardo Antelo
rawtitle: Computation of Decimal Transcendental Functions Using the {CORDIC} Algorithm
abstract:
In this work we propose new decimal floating-point CORDIC algorithms for transcendental function evaluation. We show how these algorithms are mapped to a state of the art Decimal Floating-Point Unit (DFPU), both considering the use of a carry-propagate adder or a carry-save redundant adder. We compared with previous decimal CORDIC proposals and with table-driven algorithms, and we concluded that our approach have significant potential advantages for transcendental function evaluation in state of the art DFPUs with minor modifications of the hardware.

rawabstract:
In this work we propose new decimal floating-point CORDIC algorithms for transcendental function evaluation. We show how these algorithms are mapped to a state of the art Decimal Floating-Point Unit (DFPU), both considering the use of a carry-propagate adder or a carry-save redundant adder. We compared with previous decimal CORDIC proposals and with table-driven algorithms, and we concluded that our approach have significant potential advantages for transcendental function evaluation in state of the art DFPUs with minor modifications of the hardware.

entry:
@InProceedings{Vazquez:2009:CDT,
  author =       "{\'A}lvaro V{\'a}zquez and Julio Villalba and Elisardo
                 Antelo",
  title =        "Computation of Decimal Transcendental Functions Using
                 the {CORDIC} Algorithm",
  crossref =     "Bruguera:2009:PIS",
  pages =        "179--186",
  year =         "2009",
  bibdate =      "Fri Jun 12 12:34:25 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "In this work we propose new decimal floating-point
                 CORDIC algorithms for transcendental function
                 evaluation. We show how these algorithms are mapped to
                 a state of the art Decimal Floating-Point Unit (DFPU),
                 both considering the use of a carry-propagate adder or
                 a carry-save redundant adder. We compared with previous
                 decimal CORDIC proposals and with table-driven
                 algorithms, and we concluded that our approach have
                 significant potential advantages for transcendental
                 function evaluation in state of the art DFPUs with
                 minor modifications of the hardware.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-19",
}


bibtype: article
filename: elefunt.bib
label: Weniger:2009:SHF
author: Ernst Joachim Weniger
journal: j-IJQC
volume: 109
number: 8
pages: 1728--1740
month: feb
monthnumber: 2
year: 2009
CODEN: IJQCB2
DOI: https://doi.org/10.1002/qua.22014
ISSN: 0020-7608 (print), 1097-461X (electronic) OR 00207608 (print), 1097461X (electronic)
ISSNL: 0020-7608 OR 00207608
bibdate: Fri Mar 27 07:47:31 2009
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2009.03.27 07:47:31 ???
fjournal: International Journal of Quantum Chemistry
acknowledgement: ack-nhfb
journalURL: http://www.interscience.wiley.com/jpages/0020-7608/
rawauthor: Ernst Joachim Weniger
title:
The strange history of $B$ functions or how theoretical chemists and mathematicians do (not) interact

abstract:
$B$ functions are a class of relatively complicated exponentially decaying basis functions. Because the molecular multicenter integrals of the much simpler Slater-type functions are notoriously difficult, it is not at all obvious why $B$ functions should offer any advantages. However, $B$ functions have Fourier transforms of exceptional simplicity, which greatly simplifies many of their molecular multicenter integrals. This article discusses the historical development of $B$ functions from the perspective of the interaction between mathematics and theoretical chemistry, which traditionally has not been very good. Nevertheless, future progress in theoretical chemistry depends very much on a fertile interaction with neighboring disciplines.

keywords:
B functions; electronic structure theory; exponentially decaying basis functions; interdisciplinary collaboration; multicenter integrals

rawabstract:
$B$ functions are a class of relatively complicated exponentially decaying basis functions. Because the molecular multicenter integrals of the much simpler Slater-type functions are notoriously difficult, it is not at all obvious why $B$ functions should offer any advantages. However, $B$ functions have Fourier transforms of exceptional simplicity, which greatly simplifies many of their molecular multicenter integrals. This article discusses the historical development of $B$ functions from the perspective of the interaction between mathematics and theoretical chemistry, which traditionally has not been very good. Nevertheless, future progress in theoretical chemistry depends very much on a fertile interaction with neighboring disciplines.

rawtitle:
The strange history of {$B$} functions or how theoretical chemists and mathematicians do (not) interact

entry:
@Article{Weniger:2009:SHF,
  author =       "Ernst Joachim Weniger",
  title =        "The strange history of {$B$} functions or how
                 theoretical chemists and mathematicians do (not)
                 interact",
  journal =      j-IJQC,
  volume =       "109",
  number =       "8",
  pages =        "1728--1740",
  month =        feb,
  year =         "2009",
  CODEN =        "IJQCB2",
  DOI =          "https://doi.org/10.1002/qua.22014",
  ISSN =         "0020-7608 (print), 1097-461X (electronic)",
  ISSN-L =       "0020-7608",
  bibdate =      "Fri Mar 27 07:47:31 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "$B$ functions are a class of relatively complicated
                 exponentially decaying basis functions. Because the
                 molecular multicenter integrals of the much simpler
                 Slater-type functions are notoriously difficult, it is
                 not at all obvious why $B$ functions should offer any
                 advantages. However, $B$ functions have Fourier
                 transforms of exceptional simplicity, which greatly
                 simplifies many of their molecular multicenter
                 integrals. This article discusses the historical
                 development of $B$ functions from the perspective of
                 the interaction between mathematics and theoretical
                 chemistry, which traditionally has not been very good.
                 Nevertheless, future progress in theoretical chemistry
                 depends very much on a fertile interaction with
                 neighboring disciplines.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Quantum Chemistry",
  journal-URL =  "http://www.interscience.wiley.com/jpages/0020-7608/",
  keywords =     "B functions; electronic structure theory;
                 exponentially decaying basis functions;
                 interdisciplinary collaboration; multicenter
                 integrals",
}


bibtype: article
filename: elefunt.bib
label: Wozny:2009:MSS
author: Pawel Wozny and Rafal Nowak
title: Method of summation of some slowly convergent series
journal: j-APPL-MATH-COMP
volume: 215
number: 4
pages: 1622--1645
year: 2009
CODEN: AMHCBQ
ISSN: 0096-3003 (print), 1873-5649 (electronic) OR 00963003 (print), 18735649 (electronic)
ISSNL: 0096-3003 OR 00963003
MRclass: 65B10
MRnumber: MR2571650
bibdate: Thu Dec 01 09:25:02 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2011.12.01 09:25:02 ???
fjournal: Applied Mathematics and Computation
keywords: convergence acceleration
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00963003
rawauthor: Pawe{\l} Wo{\'z}ny and Rafa{\l} Nowak
rawtitle: Method of summation of some slowly convergent series
entry:
@Article{Wozny:2009:MSS,
  author =       "Pawe{\l} Wo{\'z}ny and Rafa{\l} Nowak",
  title =        "Method of summation of some slowly convergent series",
  journal =      j-APPL-MATH-COMP,
  volume =       "215",
  number =       "4",
  pages =        "1622--1645",
  month =        "????",
  year =         "2009",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  MRclass =      "65B10",
  MRnumber =     "MR2571650",
  bibdate =      "Thu Dec 01 09:25:02 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
  keywords =     "convergence acceleration",
}


bibtype: article
filename: elefunt.bib
label: Yun:2009:ACN
author: Beong In Yun
title: Approximation to the cumulative normal distribution using hyperbolic tangent based functions
journal: Journal of the Korean Mathematical Society
volume: 46
number: 6
pages: 1267--1276
year: 2009
DOI: https://doi.org/10.4134/JKMS.2009.46.6.1267
ISSN: 0304-9914 OR 03049914
MRclass: 62E17 (65C60)
MRnumber: 2572515
bibdate: Sat Dec 16 18:04:41 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.12.16 18:04:41 ???
fjournal: Journal of the Korean Mathematical Society
acknowledgement: ack-nhfb
ajournal: J. Korean Math. Soc.
rawauthor: Beong In Yun
rawtitle: Approximation to the cumulative normal distribution using hyperbolic tangent based functions
entry:
@Article{Yun:2009:ACN,
  author =       "Beong In Yun",
  title =        "Approximation to the cumulative normal distribution
                 using hyperbolic tangent based functions",
  journal =      "Journal of the Korean Mathematical Society",
  volume =       "46",
  number =       "6",
  pages =        "1267--1276",
  year =         "2009",
  DOI =          "https://doi.org/10.4134/JKMS.2009.46.6.1267",
  ISSN =         "0304-9914",
  MRclass =      "62E17 (65C60)",
  MRnumber =     "2572515",
  bibdate =      "Sat Dec 16 18:04:41 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Korean Math. Soc.",
  fjournal =     "Journal of the Korean Mathematical Society",
}


bibtype: article
filename: elefunt.bib
label: Ahmadi:2010:LCC
author: O. Ahmadi and F. R. Henriquez
title: Low Complexity Cubing and Cube Root Computation over $ F_3^m $ in Polynomial Basis
journal: j-IEEE-TRANS-COMPUT
volume: 59
number: 10
pages: 1297--1308
month: oct
monthnumber: 10
year: 2010
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.2009.183
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sun Jul 3 11:52:32 MDT 2011
bibtimestamp: 2011.07.03 11:52:32 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5374372
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: O. Ahmadi and F. R. Henr{\'\i}quez
rawtitle: Low Complexity Cubing and Cube Root Computation over {$ F_3^m $} in Polynomial Basis
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib

entry:
@Article{Ahmadi:2010:LCC,
  author =       "O. Ahmadi and F. R. Henr{\'\i}quez",
  title =        "Low Complexity Cubing and Cube Root Computation over
                 {$ F_3^m $} in Polynomial Basis",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "59",
  number =       "10",
  pages =        "1297--1308",
  month =        oct,
  year =         "2010",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2009.183",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 3 11:52:32 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5374372",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: elefunt.bib
label: Akbarpour:2010:VSI
author: Behzad Akbarpour and Amr T. Abdel-Hamid and Sofiene Tahar and John Harrison
title: Verifying a Synthesized Implementation of IEEE-754 Floating-Point Exponential Function using HOL
journal: j-COMP-J
volume: 53
number: 4
pages: 465--488
month: may
monthnumber: 5
year: 2010
CODEN: CMPJA6
DOI: https://doi.org/10.1093/comjnl/bxp023
ISSN: 0010-4620 (print), 1460-2067 (electronic) OR 00104620 (print), 14602067 (electronic)
ISSNL: 0010-4620 OR 00104620
bibdate: Wed Apr 28 14:33:36 MDT 2010
bibtimestamp: 2010.04.28 14:33:36 MDT
fjournal: The Computer Journal
acknowledgement: ack-nhfb
journalURL: http://comjnl.oxfordjournals.org/
rawauthor: Behzad Akbarpour and Amr T. Abdel-Hamid and Sofi{\`e}ne Tahar and John Harrison
bibsource:
http://comjnl.oxfordjournals.org/content/vol53/issue4/index.dtl; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

URL:
http://comjnl.oxfordjournals.org/cgi/content/abstract/53/4/465; http://comjnl.oxfordjournals.org/cgi/reprint/53/4/465

rawtitle:
Verifying a Synthesized Implementation of {IEEE-754} Floating-Point Exponential Function using {HOL}

entry:
@Article{Akbarpour:2010:VSI,
  author =       "Behzad Akbarpour and Amr T. Abdel-Hamid and
                 Sofi{\`e}ne Tahar and John Harrison",
  title =        "Verifying a Synthesized Implementation of {IEEE-754}
                 Floating-Point Exponential Function using {HOL}",
  journal =      j-COMP-J,
  volume =       "53",
  number =       "4",
  pages =        "465--488",
  month =        may,
  year =         "2010",
  CODEN =        "CMPJA6",
  DOI =          "https://doi.org/10.1093/comjnl/bxp023",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Wed Apr 28 14:33:36 MDT 2010",
  bibsource =    "http://comjnl.oxfordjournals.org/content/vol53/issue4/index.dtl;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://comjnl.oxfordjournals.org/cgi/content/abstract/53/4/465;
                 http://comjnl.oxfordjournals.org/cgi/reprint/53/4/465",
  acknowledgement = ack-nhfb,
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
}


bibtype: article
filename: elefunt.bib
label: Alimohammad:2010:UAA
author: A. Alimohammad and S. F. Fard and B. F. Cockburn
journal: j-IEEE-TRANS-COMPUT
volume: 59
number: 4
pages: 449--456
year: 2010
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.2009.169
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sun Jul 3 11:52:27 MDT 2011
bibtimestamp: 2011.07.03 11:52:27 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5313801
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: A. Alimohammad and S. F. Fard and B. F. Cockburn
title:
A Unified Architecture for the Accurate and High-Throughput Implementation of Six Key Elementary Functions

abstract:
This paper presents a unified architecture for the compact implementation of several key elementary functions, including reciprocal, square root, and logarithm, in single-precision floating-point arithmetic. The proposed high-throughput design is based on uniform domain segmentation and curve fitting techniques. Numerically accurate least-squares regression is utilized to calculate the polynomial coefficients. The architecture is optimized by analyzing the trade-off between the size of the required memory and the precision of intermediate variables to achieve the minimum 23-bit accuracy required for single-precision floating-point representation. The efficiency of the proposed unified data path is demonstrated on a common field-programmable gate array.

rawabstract:
This paper presents a unified architecture for the compact implementation of several key elementary functions, including reciprocal, square root, and logarithm, in single-precision floating-point arithmetic. The proposed high-throughput design is based on uniform domain segmentation and curve fitting techniques. Numerically accurate least-squares regression is utilized to calculate the polynomial coefficients. The architecture is optimized by analyzing the trade-off between the size of the required memory and the precision of intermediate variables to achieve the minimum 23-bit accuracy required for single-precision floating-point representation. The efficiency of the proposed unified data path is demonstrated on a common field-programmable gate array.

rawtitle:
A Unified Architecture for the Accurate and High-Throughput Implementation of Six Key Elementary Functions

entry:
@Article{Alimohammad:2010:UAA,
  author =       "A. Alimohammad and S. F. Fard and B. F. Cockburn",
  title =        "A Unified Architecture for the Accurate and
                 High-Throughput Implementation of Six Key Elementary
                 Functions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "59",
  number =       "4",
  pages =        "449--456",
  month =        "????",
  year =         "2010",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2009.169",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 3 11:52:27 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5313801",
  abstract =     "This paper presents a unified architecture for the
                 compact implementation of several key elementary
                 functions, including reciprocal, square root, and
                 logarithm, in single-precision floating-point
                 arithmetic. The proposed high-throughput design is
                 based on uniform domain segmentation and curve fitting
                 techniques. Numerically accurate least-squares
                 regression is utilized to calculate the polynomial
                 coefficients. The architecture is optimized by
                 analyzing the trade-off between the size of the
                 required memory and the precision of intermediate
                 variables to achieve the minimum 23-bit accuracy
                 required for single-precision floating-point
                 representation. The efficiency of the proposed unified
                 data path is demonstrated on a common
                 field-programmable gate array.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: elefunt.bib
label: Alzer:2010:EFI
author: Horst Alzer
title: Error function inequalities
journal: j-ADV-COMPUT-MATH
volume: 33
number: 3
pages: 349--379
month: oct
monthnumber: 10
year: 2010
CODEN: ACMHEX
DOI: https://doi.org/10.1007/s10444-009-9139-2
ISSN: 1019-7168 (print), 1572-9044 (electronic) OR 10197168 (print), 15729044 (electronic)
ISSNL: 1019-7168 OR 10197168
MRclass: 33B20 (26D07 26D15)
MRnumber: 2718103
MRreviewer: Feng Qi
bibdate: Sat Feb 3 18:22:50 MST 2018
bibtimestamp: 2018.02.03 18:22:50 MST
URL: http://link.springer.com/article/10.1007/s10444-009-9139-2
fjournal: Advances in Computational Mathematics
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10444
rawauthor: Horst Alzer
rawtitle: Error function inequalities
bibsource:
https://www.math.utah.edu/pub/tex/bib/advcomputmath.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Alzer:2010:EFI,
  author =       "Horst Alzer",
  title =        "Error function inequalities",
  journal =      j-ADV-COMPUT-MATH,
  volume =       "33",
  number =       "3",
  pages =        "349--379",
  month =        oct,
  year =         "2010",
  CODEN =        "ACMHEX",
  DOI =          "https://doi.org/10.1007/s10444-009-9139-2",
  ISSN =         "1019-7168 (print), 1572-9044 (electronic)",
  ISSN-L =       "1019-7168",
  MRclass =      "33B20 (26D07 26D15)",
  MRnumber =     "2718103",
  MRreviewer =   "Feng Qi",
  bibdate =      "Sat Feb 3 18:22:50 MST 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/advcomputmath.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://link.springer.com/article/10.1007/s10444-009-9139-2",
  acknowledgement = ack-nhfb,
  fjournal =     "Advances in Computational Mathematics",
  journal-URL =  "http://link.springer.com/journal/10444",
}


bibtype: article
filename: elefunt.bib
label: Anand:2010:UTE
author: Christopher Kumar Anand and Anuroop Sharma
title: Unified Tables for Exponential and Logarithm Families
journal: j-TOMS
volume: 37
number: 3
pages: 28:1--28:23
month: sep
monthnumber: 9
year: 2010
CODEN: ACMSCU
DOI: https://doi.org/10.1145/1824801.1824806
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Mon Sep 27 10:15:50 MDT 2010
bibtimestamp: 2010.09.27 10:15:50 MDT
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: Accurate tables method; Cell/B.E; IEEE arithmetic; SIMD; vector library
acknowledgement: ack-nhfb
articleno: 28
journalURL: https://dl.acm.org/loi/toms
rawauthor: Christopher Kumar Anand and Anuroop Sharma
rawtitle: Unified Tables for Exponential and Logarithm Families
abstract:
Accurate table methods allow for very accurate and efficient evaluation of elementary functions. We present new single-table approaches to logarithm and exponential evaluation, by which we mean that a single table of values works for both $ log (x) $ and $ l o g(1 + x) $, and a single table for $ e^x $ and $ e^x - 1 $. This approach eliminates special cases normally required to evaluate $ log (1 + x) $ and $ e^x - 1 $ accurately near zero, which will significantly improve performance on architectures which use SIMD parallelism, or on which data-dependent branching is expensive.par We have implemented it on the Cell/B.E. SPU (SIMD compute engine) and found the resulting functions to be up to twice as fast as the conventional implementations distributed in the IBM Mathematical Acceleration Subsystem (MASS). We include the literate code used to generate all the variants of exponential and log functions in the article, and discuss relevant language and hardware features.

rawabstract:
Accurate table methods allow for very accurate and efficient evaluation of elementary functions. We present new single-table approaches to logarithm and exponential evaluation, by which we mean that a single table of values works for both $ \log (x) $ and $ l o g(1 + x) $, and a single table for $ e^x $ and $ e^x - 1 $. This approach eliminates special cases normally required to evaluate $ \log (1 + x) $ and $ e^x - 1 $ accurately near zero, which will significantly improve performance on architectures which use SIMD parallelism, or on which data-dependent branching is expensive.\par We have implemented it on the Cell/B.E. SPU (SIMD compute engine) and found the resulting functions to be up to twice as fast as the conventional implementations distributed in the IBM Mathematical Acceleration Subsystem (MASS). We include the literate code used to generate all the variants of exponential and log functions in the article, and discuss relevant language and hardware features.

entry:
@Article{Anand:2010:UTE,
  author =       "Christopher Kumar Anand and Anuroop Sharma",
  title =        "Unified Tables for Exponential and Logarithm
                 Families",
  journal =      j-TOMS,
  volume =       "37",
  number =       "3",
  pages =        "28:1--28:23",
  month =        sep,
  year =         "2010",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1824801.1824806",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Sep 27 10:15:50 MDT 2010",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Accurate table methods allow for very accurate and
                 efficient evaluation of elementary functions. We
                 present new single-table approaches to logarithm and
                 exponential evaluation, by which we mean that a single
                 table of values works for both $ \log (x) $ and $ l o
                 g(1 + x) $, and a single table for $ e^x $ and $ e^x -
                 1 $. This approach eliminates special cases normally
                 required to evaluate $ \log (1 + x) $ and $ e^x - 1 $
                 accurately near zero, which will significantly improve
                 performance on architectures which use SIMD
                 parallelism, or on which data-dependent branching is
                 expensive.\par

                 We have implemented it on the Cell/B.E. SPU (SIMD
                 compute engine) and found the resulting functions to be
                 up to twice as fast as the conventional implementations
                 distributed in the IBM Mathematical Acceleration
                 Subsystem (MASS). We include the literate code used to
                 generate all the variants of exponential and log
                 functions in the article, and discuss relevant language
                 and hardware features.",
  acknowledgement = ack-nhfb,
  articleno =    "28",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Accurate tables method; Cell/B.E; IEEE arithmetic;
                 SIMD; vector library",
}


bibtype: book
filename: elefunt.bib
label: Baricz:2010:GBF
author: Arpad Baricz
title: Generalized Bessel Functions of the First Kind
volume: 1994
publisher: pub-SV
address: pub-SV:adr
pages: xiv + 206
year: 2010
CODEN: LNMAA2
DOI: https://doi.org/10.1007/978-3-642-12230-9
ISBN: 3-642-12229-9 (print), 3-642-12230-2 (e-book) OR 3642122299 (print), 3642122302 (ebook)
ISSN: 0075-8434 (print), 1617-9692 (electronic) OR 00758434 (print), 16179692 (electronic)
ISSNL: 0075-8434 OR 00758434
LCCN: QA3 .L28 no. 1994
MRclass: 33C10 (33-02 33C05 33C75)
MRnumber: 2656410 (2011f:33007)
MRreviewer: Matti Vuorinen
bibdate: Tue May 6 14:56:34 MDT 2014
bibtimestamp: 2014.05.06 14:56:34 MDT
series: ser-LECT-NOTES-MATH
acknowledgement: ack-nhfb
rawauthor: {\'A}rp{\'a}d Baricz
rawtitle: Generalized {Bessel} Functions of the First Kind
ISBN13:
978-3-642-12229-3 (print), 978-3-642-12230-9 (e-book) OR 9783642122293 (print), 9783642122309 (ebook)

bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/lnm2010.bib

URL:
http://link.springer.com/book/10.1007/978-3-642-12230-9; http://www.springerlink.com/content/978-3-642-12230-9

entry:
@Book{Baricz:2010:GBF,
  author =       "{\'A}rp{\'a}d Baricz",
  title =        "Generalized {Bessel} Functions of the First Kind",
  volume =       "1994",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xiv + 206",
  year =         "2010",
  CODEN =        "LNMAA2",
  DOI =          "https://doi.org/10.1007/978-3-642-12230-9",
  ISBN =         "3-642-12229-9 (print), 3-642-12230-2 (e-book)",
  ISBN-13 =      "978-3-642-12229-3 (print), 978-3-642-12230-9
                 (e-book)",
  ISSN =         "0075-8434 (print), 1617-9692 (electronic)",
  ISSN-L =       "0075-8434",
  LCCN =         "QA3 .L28 no. 1994",
  MRclass =      "33C10 (33-02 33C05 33C75)",
  MRnumber =     "2656410 (2011f:33007)",
  MRreviewer =   "Matti Vuorinen",
  bibdate =      "Tue May 6 14:56:34 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/lnm2010.bib",
  series =       ser-LECT-NOTES-MATH,
  URL =          "http://link.springer.com/book/10.1007/978-3-642-12230-9;
                 http://www.springerlink.com/content/978-3-642-12230-9",
  acknowledgement = ack-nhfb,
  series-URL =   "http://link.springer.com/bookseries/304",
}


bibtype: article
filename: elefunt.bib
label: Baricz:2010:GPG
author: Arpad Baricz
title: Geometric Properties of Generalized Bessel Functions
journal: j-LECT-NOTES-MATH
volume: 1994
pages: 23--69
year: 2010
CODEN: LNMAA2
DOI: https://doi.org/10.1007/978-3-642-12230-9_2
ISBN: 3-642-12229-9 (print), 3-642-12230-2 (e-book) OR 3642122299 (print), 3642122302 (ebook)
ISSN: 0075-8434 (print), 1617-9692 (electronic) OR 00758434 (print), 16179692 (electronic)
ISSNL: 0075-8434 OR 00758434
bibdate: Fri May 9 19:06:58 MDT 2014
bibtimestamp: 2014.05.09 19:06:58 MDT
URL: http://link.springer.com/content/pdf/10.1007/978-3-642-12230-9_2.pdf
fjournal: Lecture Notes in Mathematics
acknowledgement: ack-nhfb
bookDOI: https://doi.org/10.1007/978-3-642-12230-9
bookURL: http://www.springerlink.com/content/978-3-642-12230-9
journalURL: http://link.springer.com/bookseries/304
rawauthor: {\'A}rp{\'a}d Baricz
rawtitle: Geometric Properties of Generalized {Bessel} Functions
ISBN13:
978-3-642-12229-3 (print), 978-3-642-12230-9 (e-book) OR 9783642122293 (print), 9783642122309 (ebook)

bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/lnm2010.bib

entry:
@Article{Baricz:2010:GPG,
  author =       "{\'A}rp{\'a}d Baricz",
  title =        "Geometric Properties of Generalized {Bessel}
                 Functions",
  journal =      j-LECT-NOTES-MATH,
  volume =       "1994",
  pages =        "23--69",
  year =         "2010",
  CODEN =        "LNMAA2",
  DOI =          "https://doi.org/10.1007/978-3-642-12230-9_2",
  ISBN =         "3-642-12229-9 (print), 3-642-12230-2 (e-book)",
  ISBN-13 =      "978-3-642-12229-3 (print), 978-3-642-12230-9
                 (e-book)",
  ISSN =         "0075-8434 (print), 1617-9692 (electronic)",
  ISSN-L =       "0075-8434",
  bibdate =      "Fri May 9 19:06:58 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/lnm2010.bib",
  URL =          "http://link.springer.com/content/pdf/10.1007/978-3-642-12230-9_2.pdf",
  acknowledgement = ack-nhfb,
  book-DOI =     "https://doi.org/10.1007/978-3-642-12230-9",
  book-URL =     "http://www.springerlink.com/content/978-3-642-12230-9",
  fjournal =     "Lecture Notes in Mathematics",
  journal-URL =  "http://link.springer.com/bookseries/304",
}


bibtype: book
filename: elefunt.bib
label: Beals:2010:SFG
author: Richard Beals and R. (Roderick) Wong
title: Special functions: a graduate text
volume: 126
publisher: pub-CAMBRIDGE
address: pub-CAMBRIDGE:adr
pages: ix + 456
year: 2010
ISBN: 0-521-19797-X OR 052119797X
ISBN13: 978-0-521-19797-7 OR 9780521197977
LCCN: QA351 .B34 2010; QA351 BEA 2010
bibdate: Sat Oct 30 16:43:46 MDT 2010
bibtimestamp: 2010.10.30 16:43:46 MDT
series: Cambridge studies in advanced mathematics
subject: Functions, Special; Textbooks
acknowledgement: ack-nhfb
rawauthor: Richard Beals and R. (Roderick) Wong
rawtitle: Special functions: a graduate text
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/mathcw.bib; library.ox.ac.uk:210/ADVANCE

URL:
http://assets.cambridge.org/97805211/97977/cover/9780521197977.jpg; http://www.loc.gov/catdir/enhancements/fy1009/2010017815-b.html; http://www.loc.gov/catdir/enhancements/fy1009/2010017815-d.html; http://www.loc.gov/catdir/enhancements/fy1009/2010017815-t.html

abstract:
From the Publisher: The subject of special functions is often presented as a collection of disparate results, which are rarely organised in a coherent way. This book answers the need for a different approach to the subject. The authors' main goals are to emphasise general unifying principles coherently and to provide clear motivation, efficient proofs, and original references for all of the principal results. The book covers standard material, but also much more, including chapters on discrete orthogonal polynomials and elliptic functions. The authors show how a very large part of the subject traces back to two equations --- the hypergeometric equation and the confluent hypergeometric equation --- and describe the various ways in which these equations are canonical and special. Providing ready access to theory and formulas, this book serves as an ideal graduate-level textbook as well as a convenient reference.

TOC:
Preface; 1. Orientation 2. Gamma, beta, zeta 3. Second order differential equations 4. Orthogonal polynomials 5. Discrete orthogonal polynomials 6. Confluent hypergeometric functions 7. Cylinder functions 8. Hypergeometric functions 9. Spherical functions 10. Asymptotics 11. Elliptic functions References Index

rawabstract:
From the Publisher: The subject of special functions is often presented as a collection of disparate results, which are rarely organised in a coherent way. This book answers the need for a different approach to the subject. The authors' main goals are to emphasise general unifying principles coherently and to provide clear motivation, efficient proofs, and original references for all of the principal results. The book covers standard material, but also much more, including chapters on discrete orthogonal polynomials and elliptic functions. The authors show how a very large part of the subject traces back to two equations --- the hypergeometric equation and the confluent hypergeometric equation --- and describe the various ways in which these equations are canonical and special. Providing ready access to theory and formulas, this book serves as an ideal graduate-level textbook as well as a convenient reference.

rawTOC:
Preface; 1. Orientation\\ 2. Gamma, beta, zeta\\ 3. Second order differential equations\\ 4. Orthogonal polynomials\\ 5. Discrete orthogonal polynomials\\ 6. Confluent hypergeometric functions\\ 7. Cylinder functions\\ 8. Hypergeometric functions\\ 9. Spherical functions\\ 10. Asymptotics\\ 11. Elliptic functions\\ References\\ Index

entry:
@Book{Beals:2010:SFG,
  author =       "Richard Beals and R. (Roderick) Wong",
  title =        "Special functions: a graduate text",
  volume =       "126",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  pages =        "ix + 456",
  year =         "2010",
  ISBN =         "0-521-19797-X",
  ISBN-13 =      "978-0-521-19797-7",
  LCCN =         "QA351 .B34 2010; QA351 BEA 2010",
  bibdate =      "Sat Oct 30 16:43:46 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
                 library.ox.ac.uk:210/ADVANCE",
  series =       "Cambridge studies in advanced mathematics",
  URL =          "http://assets.cambridge.org/97805211/97977/cover/9780521197977.jpg;
                 http://www.loc.gov/catdir/enhancements/fy1009/2010017815-b.html;
                 http://www.loc.gov/catdir/enhancements/fy1009/2010017815-d.html;
                 http://www.loc.gov/catdir/enhancements/fy1009/2010017815-t.html",
  abstract =     "From the Publisher: The subject of special functions
                 is often presented as a collection of disparate
                 results, which are rarely organised in a coherent way.
                 This book answers the need for a different approach to
                 the subject. The authors' main goals are to emphasise
                 general unifying principles coherently and to provide
                 clear motivation, efficient proofs, and original
                 references for all of the principal results. The book
                 covers standard material, but also much more, including
                 chapters on discrete orthogonal polynomials and
                 elliptic functions. The authors show how a very large
                 part of the subject traces back to two equations ---
                 the hypergeometric equation and the confluent
                 hypergeometric equation --- and describe the various
                 ways in which these equations are canonical and
                 special. Providing ready access to theory and formulas,
                 this book serves as an ideal graduate-level textbook as
                 well as a convenient reference.",
  acknowledgement = ack-nhfb,
  subject =      "Functions, Special; Textbooks",
  tableofcontents = "Preface; 1. Orientation\\
                 2. Gamma, beta, zeta\\
                 3. Second order differential equations\\
                 4. Orthogonal polynomials\\
                 5. Discrete orthogonal polynomials\\
                 6. Confluent hypergeometric functions\\
                 7. Cylinder functions\\
                 8. Hypergeometric functions\\
                 9. Spherical functions\\
                 10. Asymptotics\\
                 11. Elliptic functions\\
                 References\\
                 Index",
}


bibtype: inproceedings
filename: elefunt.bib
label: Benoit:2010:DDM
title: The Dynamic Dictionary of Mathematical Functions (DDMF)
crossref: Fukuda:2010:MSI
pages: 35--41
year: 2010
DOI: https://doi.org/10.1007/978-3-642-15582-6_7
bibdate: Sat Sep 23 06:20:46 2023
bibtimestamp: 2023.09.23 06:20:46 ???
acknowledgement: ack-nhfb
rawtitle: The Dynamic Dictionary of Mathematical Functions {(DDMF)}
author:
Alexandre Benoit and Frederic Chyzak and Alexis Darrasse and Stefan Gerhold and Marc Mezzarobba and Bruno Salvy

rawauthor:
Alexandre Benoit and Fr{\'e}d{\'e}ric Chyzak and Alexis Darrasse and Stefan Gerhold and Marc Mezzarobba and Bruno Salvy

entry:
@InProceedings{Benoit:2010:DDM,
  author =       "Alexandre Benoit and Fr{\'e}d{\'e}ric Chyzak and
                 Alexis Darrasse and Stefan Gerhold and Marc Mezzarobba
                 and Bruno Salvy",
  title =        "The Dynamic Dictionary of Mathematical Functions
                 {(DDMF)}",
  crossref =     "Fukuda:2010:MSI",
  pages =        "35--41",
  year =         "2010",
  DOI =          "https://doi.org/10.1007/978-3-642-15582-6_7",
  bibdate =      "Sat Sep 23 06:20:46 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Borghi:2010:AFE
author: Riccardo Borghi
title: Asymptotic and factorial expansions of Euler series truncation errors via exponential polynomials
journal: j-APPL-NUM-MATH
volume: 60
number: 12
pages: 1242--1250
month: dec
monthnumber: 12
year: 2010
CODEN: ANMAEL
ISSN: 0168-9274 (print), 1873-5460 (electronic) OR 01689274 (print), 18735460 (electronic)
ISSNL: 0168-9274 OR 01689274
MRclass: 65B10 (33F05 40A25)
MRnumber: MR2735157
bibdate: Thu Dec 01 09:47:34 2011
bibtimestamp: 2011.12.01 09:47:34 ???
fjournal: Applied Numerical Mathematics: Transactions of IMACS
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/01689274/
rawauthor: Riccardo Borghi
rawtitle: Asymptotic and factorial expansions of {Euler} series truncation errors via exponential polynomials
entry:
@Article{Borghi:2010:AFE,
  author =       "Riccardo Borghi",
  title =        "Asymptotic and factorial expansions of {Euler} series
                 truncation errors via exponential polynomials",
  journal =      j-APPL-NUM-MATH,
  volume =       "60",
  number =       "12",
  pages =        "1242--1250",
  month =        dec,
  year =         "2010",
  CODEN =        "ANMAEL",
  ISSN =         "0168-9274 (print), 1873-5460 (electronic)",
  ISSN-L =       "0168-9274",
  MRclass =      "65B10 (33F05 40A25)",
  MRnumber =     "MR2735157",
  bibdate =      "Thu Dec 01 09:47:34 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applnummath.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Numerical Mathematics: Transactions of IMACS",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01689274/",
}


bibtype: article
filename: elefunt.bib
label: Brent:2010:UAE
author: Richard P. Brent
title: Unrestricted algorithms for elementary and special functions
journal: arxiv.org
pages: 1--13
month: apr
monthnumber: 4
year: 2010
bibdate: Sat Feb 25 10:56:45 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.02.25 10:56:45 ???
URL: https://arxiv.org/abs/1004.3621
acknowledgement: ack-nhfb
rawauthor: Richard P. Brent
rawtitle: Unrestricted algorithms for elementary and special functions
abstract:
We describe some ``unrestricted'' algorithms which are useful for the computation of elementary and special functions when the precision required is not known in advance. Several general classes of algorithms are identified and illustrated by examples. The topics include: power series methods, use of halving identities, asymptotic expansions, continued fractions, recurrence relations, Newton's method, numerical contour integration, and the arithmetic-geometric mean. Most of the algorithms discussed are implemented in the MP package.

rawabstract:
We describe some ``unrestricted'' algorithms which are useful for the computation of elementary and special functions when the precision required is not known in advance. Several general classes of algorithms are identified and illustrated by examples. The topics include: power series methods, use of halving identities, asymptotic expansions, continued fractions, recurrence relations, Newton's method, numerical contour integration, and the arithmetic-geometric mean. Most of the algorithms discussed are implemented in the MP package.

entry:
@Article{Brent:2010:UAE,
  author =       "Richard P. Brent",
  title =        "Unrestricted algorithms for elementary and special
                 functions",
  journal =      "arxiv.org",
  volume =       "??",
  number =       "??",
  pages =        "1--13",
  month =        apr,
  year =         "2010",
  bibdate =      "Sat Feb 25 10:56:45 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://arxiv.org/abs/1004.3621",
  abstract =     "We describe some ``unrestricted'' algorithms which are
                 useful for the computation of elementary and special
                 functions when the precision required is not known in
                 advance. Several general classes of algorithms are
                 identified and illustrated by examples. The topics
                 include: power series methods, use of halving
                 identities, asymptotic expansions, continued fractions,
                 recurrence relations, Newton's method, numerical
                 contour integration, and the arithmetic-geometric mean.
                 Most of the algorithms discussed are implemented in the
                 MP package.",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Celledoni:2010:AFF
author: Elena Celledoni and Antonella Zanna
title: Algorithm 903: FRB --- Fortran routines for the exact computation of free rigid body motions
journal: j-TOMS
volume: 37
number: 2
pages: 23:1--23:24
month: apr
monthnumber: 4
year: 2010
CODEN: ACMSCU
DOI: https://doi.org/10.1145/1731022.1731033
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Wed Apr 21 11:39:57 MDT 2010
bibtimestamp: 2010.04.21 11:39:57 MDT
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: attitude rotation; Jacobi elliptic integrals; numerical methods; Rigid body; splitting methods
acknowledgement: ack-nhfb
articleno: 23
journalURL: https://dl.acm.org/loi/toms
rawauthor: Elena Celledoni and Antonella Zanna
rawtitle: {Algorithm 903}: {FRB} --- {Fortran} routines for the exact computation of free rigid body motions
abstract:
We present two algorithms and their corresponding Fortran routines for the exact computation of free rigid body motions. The methods use the same description of the angular momentum part $m$ by Jacobi elliptic functions, and suitably chosen frames for the attitude matrix / quaternion $ Q / q $, respectively. The frame transformation requires the computation of elliptic integrals of the third kind. Implementation and usage of the routines are described, and some examples of drivers are included. Accuracy and performance are also tested to provide reliable numerical results.

rawabstract:
We present two algorithms and their corresponding Fortran routines for the exact computation of free rigid body motions. The methods use the same description of the angular momentum part $m$ by Jacobi elliptic functions, and suitably chosen frames for the attitude matrix\slash quaternion $ Q / q $, respectively. The frame transformation requires the computation of elliptic integrals of the third kind. Implementation and usage of the routines are described, and some examples of drivers are included. Accuracy and performance are also tested to provide reliable numerical results.

entry:
@Article{Celledoni:2010:AFF,
  author =       "Elena Celledoni and Antonella Zanna",
  title =        "{Algorithm 903}: {FRB} --- {Fortran} routines for the
                 exact computation of free rigid body motions",
  journal =      j-TOMS,
  volume =       "37",
  number =       "2",
  pages =        "23:1--23:24",
  month =        apr,
  year =         "2010",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1731022.1731033",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Apr 21 11:39:57 MDT 2010",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We present two algorithms and their corresponding
                 Fortran routines for the exact computation of free
                 rigid body motions. The methods use the same
                 description of the angular momentum part $m$ by Jacobi
                 elliptic functions, and suitably chosen frames for the
                 attitude matrix\slash quaternion $ Q / q $,
                 respectively. The frame transformation requires the
                 computation of elliptic integrals of the third kind.
                 Implementation and usage of the routines are described,
                 and some examples of drivers are included. Accuracy and
                 performance are also tested to provide reliable
                 numerical results.",
  acknowledgement = ack-nhfb,
  articleno =    "23",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "attitude rotation; Jacobi elliptic integrals;
                 numerical methods; Rigid body; splitting methods",
}


bibtype: article
filename: elefunt.bib
label: Cuyt:2010:VSF
author: Annie Cuyt and Franky Backeljauw and Stefan Becuwe and Joris Van Deun
title: Validated Special Functions Software
journal: j-LECT-NOTES-COMP-SCI
volume: 6327
pages: 32--34
year: 2010
CODEN: LNCSD9
DOI: https://doi.org/10.1007/978-3-642-15582-6_6
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Sat Aug 9 15:34:11 MDT 2014
bibtimestamp: 2014.08.09 15:34:11 MDT
URL: http://link.springer.com/content/pdf/10.1007/978-3-642-15582-6_6.pdf
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
bookDOI: https://doi.org/10.1007/978-3-642-15582-6
bookURL: http://www.springerlink.com/content/978-3-642-15582-6
journalURL: http://link.springer.com/bookseries/558
rawauthor: Annie Cuyt and Franky Backeljauw and Stefan Becuwe and Joris {Van Deun}
rawtitle: Validated Special Functions Software
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/lncs2010a.bib

entry:
@Article{Cuyt:2010:VSF,
  author =       "Annie Cuyt and Franky Backeljauw and Stefan Becuwe and
                 Joris {Van Deun}",
  title =        "Validated Special Functions Software",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "6327",
  pages =        "32--34",
  year =         "2010",
  CODEN =        "LNCSD9",
  DOI =          "https://doi.org/10.1007/978-3-642-15582-6_6",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Aug 9 15:34:11 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/lncs2010a.bib",
  URL =          "http://link.springer.com/content/pdf/10.1007/978-3-642-15582-6_6.pdf",
  acknowledgement = ack-nhfb,
  book-DOI =     "https://doi.org/10.1007/978-3-642-15582-6",
  book-URL =     "http://www.springerlink.com/content/978-3-642-15582-6",
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: inproceedings
filename: elefunt.bib
label: deDinechin:2010:FPE
author: Florent de Dinechin and Bogdan Pasca
editor: Jinian Bian and Qiang Zhou and Kang Zhao
title: Floating-point exponential functions for DSP-enabled FPGAs
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 110--117
month: dec
monthnumber: 12
year: 2010
DOI: https://doi.org/10.1109/FPT.2010.5681764
bibdate: Sat Feb 08 09:35:06 2020
bibtimestamp: 2020.02.08 09:35:06 ???
acknowledgement: ack-nhfb
rawauthor: Florent de Dinechin and Bogdan Pasca
raweditor: Jinian Bian and Qiang Zhou and Kang Zhao
rawtitle: Floating-point exponential functions for {DSP}-enabled {FPGAs}
booktitle:
Proceedings 2010 International Conference on Field-Programmable Technology, 8--10 December 2010, Beijing, China

rawbooktitle:
{Proceedings 2010 International Conference on Field-Programmable Technology, 8--10 December 2010, Beijing, China}

entry:
@InProceedings{deDinechin:2010:FPE,
  author =       "Florent de Dinechin and Bogdan Pasca",
  editor =       "Jinian Bian and Qiang Zhou and Kang Zhao",
  booktitle =    "{Proceedings 2010 International Conference on
                 Field-Programmable Technology, 8--10 December 2010,
                 Beijing, China}",
  title =        "Floating-point exponential functions for {DSP}-enabled
                 {FPGAs}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "110--117",
  month =        dec,
  year =         "2010",
  DOI =          "https://doi.org/10.1109/FPT.2010.5681764",
  bibdate =      "Sat Feb 08 09:35:06 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Dumbgen:2010:BSG
author: L. Dumbgen
title: Bounding standard Gaussian tail probabilities
journal: arxiv.org
pages: ??--??
day: 9
month: dec
monthnumber: 12
year: 2010
bibdate: Sat Dec 16 16:24:48 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.12.16 16:24:48 ???
URL: https://arxiv.org/abs/1012.2063
acknowledgement: ack-nhfb
rawauthor: L. D{\"u}mbgen
rawtitle: Bounding standard {Gaussian} tail probabilities
entry:
@Article{Dumbgen:2010:BSG,
  author =       "L. D{\"u}mbgen",
  title =        "Bounding standard {Gaussian} tail probabilities",
  journal =      "arxiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "9",
  month =        dec,
  year =         "2010",
  bibdate =      "Sat Dec 16 16:24:48 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://arxiv.org/abs/1012.2063",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: elefunt.bib
label: Erocal:2010:SPU
author: Burcin Erocal and William Stein
crossref: Fukuda:2010:MSI
pages: 12--27
year: 2010
DOI: https://doi.org/10.1007/978-3-642-15582-6_4
bibdate: Sat Sep 23 06:20:46 2023
bibtimestamp: 2023.09.23 06:20:46 ???
acknowledgement: ack-nhfb
rawauthor: Bur{\c{c}}in Er{\"o}cal and William Stein
title:
The Sage Project: Unifying Free Mathematical Software to Create a Viable Alternative to Magma, Maple, Mathematica and MATLAB

bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/magma.bib; https://www.math.utah.edu/pub/tex/bib/maple-extract.bib; https://www.math.utah.edu/pub/tex/bib/mathematica.bib; https://www.math.utah.edu/pub/tex/bib/matlab.bib

rawtitle:
The {Sage Project}: Unifying Free Mathematical Software to Create a Viable Alternative to {Magma}, {Maple}, {Mathematica} and {MATLAB}

entry:
@InProceedings{Erocal:2010:SPU,
  author =       "Bur{\c{c}}in Er{\"o}cal and William Stein",
  title =        "The {Sage Project}: Unifying Free Mathematical
                 Software to Create a Viable Alternative to {Magma},
                 {Maple}, {Mathematica} and {MATLAB}",
  crossref =     "Fukuda:2010:MSI",
  pages =        "12--27",
  year =         "2010",
  DOI =          "https://doi.org/10.1007/978-3-642-15582-6_4",
  bibdate =      "Sat Sep 23 06:20:46 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/magma.bib;
                 https://www.math.utah.edu/pub/tex/bib/maple-extract.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathematica.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Fukushima:2010:FCI
author: Toshio Fukushima
title: Fast computation of incomplete elliptic integral of first kind by half argument transformation
journal: j-NUM-MATH
volume: 116
number: 4
pages: 687--719
month: oct
monthnumber: 10
year: 2010
CODEN: NUMMA7
DOI: https://doi.org/10.1007/s00211-010-0321-8
ISSN: 0029-599X (print), 0945-3245 (electronic) OR 0029599X (print), 09453245 (electronic)
ISSNL: 0029-599X OR 0029599X
bibdate: Sat Oct 16 16:02:41 MDT 2010
bibtimestamp: 2010.10.16 16:02:41 MDT
URL: http://www.springerlink.com/openurl.asp?genre=article&issn=0029-599X&volume=116&issue=4&spage=687
fjournal: Numerische Mathematik
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/211
rawauthor: Toshio Fukushima
rawtitle: Fast computation of incomplete elliptic integral of first kind by half argument transformation
bibsource:
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0029-599X&volume=116&issue=4; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

abstract:
We developed a new method to calculate the incomplete elliptic integral of the first kind, $ F(varphi |m) $, by using the half argument formulas of Jacobian elliptic functions. The method reduces the magnitude of $ varphi $ by repeated usage of the formulas while fixing $m$. The method is sufficiently precise in the sense that the maximum relative error is $3$--$5$ machine epsilons at most. Thanks to the simplicity of the half argument formulas, the new procedure is significantly faster than the existing procedures. For example, it runs 20--60% faster than Bulirsch's function, tt el1, and 1.9--2.2 times faster than the method using Carlson's function, $ R_F $.

rawabstract:
We developed a new method to calculate the incomplete elliptic integral of the first kind, $ F(\varphi |m) $, by using the half argument formulas of Jacobian elliptic functions. The method reduces the magnitude of $ \varphi $ by repeated usage of the formulas while fixing $m$. The method is sufficiently precise in the sense that the maximum relative error is $3$--$5$ machine epsilons at most. Thanks to the simplicity of the half argument formulas, the new procedure is significantly faster than the existing procedures. For example, it runs 20--60\% faster than Bulirsch's function, {\tt el1}, and 1.9--2.2 times faster than the method using Carlson's function, $ R_F $.

entry:
@Article{Fukushima:2010:FCI,
  author =       "Toshio Fukushima",
  title =        "Fast computation of incomplete elliptic integral of
                 first kind by half argument transformation",
  journal =      j-NUM-MATH,
  volume =       "116",
  number =       "4",
  pages =        "687--719",
  month =        oct,
  year =         "2010",
  CODEN =        "NUMMA7",
  DOI =          "https://doi.org/10.1007/s00211-010-0321-8",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Sat Oct 16 16:02:41 MDT 2010",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0029-599X&volume=116&issue=4;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0029-599X&volume=116&issue=4&spage=687",
  abstract =     "We developed a new method to calculate the incomplete
                 elliptic integral of the first kind, $ F(\varphi |m) $,
                 by using the half argument formulas of Jacobian
                 elliptic functions. The method reduces the magnitude of
                 $ \varphi $ by repeated usage of the formulas while
                 fixing $m$. The method is sufficiently precise in the
                 sense that the maximum relative error is $3$--$5$
                 machine epsilons at most. Thanks to the simplicity of
                 the half argument formulas, the new procedure is
                 significantly faster than the existing procedures. For
                 example, it runs 20--60\% faster than Bulirsch's
                 function, {\tt el1}, and 1.9--2.2 times faster than the
                 method using Carlson's function, $ R_F $.",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}


bibtype: book
filename: elefunt.bib
label: ISO:2010:IIIa
author: ISO
publisher: pub-ISO
address: pub-ISO:adr
pages: 687--719
year: 2010
bibdate: Thu Nov 25 08:56:44 2010
bibtimestamp: 2010.11.25 08:56:44 ???
series: Technical report
URL: http://www.iso.org/iso/iso_catalogue/catalogue_tc/catalogue_detail.htm?csnumber=50511
subject: programming languages (electronic computers)
acknowledgement: ack-nhfb
rawauthor: {ISO}
title:
ISO / IEC 29124:2010: Information technology --- Programming languages, their environments and system software interfaces --- Extensions to the C++ Library to support mathematical special functions

bibsource:
http://www.iso.org/iso/search.htm; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/isostd.bib

rawtitle:
{ISO\slash IEC 29124:2010}: Information technology --- Programming languages, their environments and system software interfaces --- Extensions to the {C++ Library} to support mathematical special functions

entry:
@Book{ISO:2010:IIIa,
  author =       "{ISO}",
  title =        "{ISO\slash IEC 29124:2010}: Information technology ---
                 Programming languages, their environments and system
                 software interfaces --- Extensions to the {C++ Library}
                 to support mathematical special functions",
  publisher =    pub-ISO,
  address =      pub-ISO:adr,
  year =         "2010",
  LCCN =         "????",
  bibdate =      "Thu Nov 25 08:56:44 2010",
  bibsource =    "http://www.iso.org/iso/search.htm;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/isostd.bib",
  series =       "Technical report",
  URL =          "http://www.iso.org/iso/iso_catalogue/catalogue_tc/catalogue_detail.htm?csnumber=50511",
  acknowledgement = ack-nhfb,
  subject =      "programming languages (electronic computers)",
}


bibtype: article
filename: elefunt.bib
label: Li:2010:NRB
author: Rong Li and Pooi Yuen Kam and Hua Fu
journal: j-IEEE-TRANS-COMM
volume: 58
number: 1
pages: 157--169
month: jan
monthnumber: 1
year: 2010
CODEN: IECMBT
DOI: https://doi.org/10.1109/tcomm.2010.01.070426
ISSN: 0090-6778 (print), 1558-0857 (electronic) OR 00906778 (print), 15580857 (electronic)
ISSNL: 0090-6778 OR 00906778
bibdate: Sat Dec 16 16:52:49 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.12.16 16:52:49 ???
URL: http://ieeexplore.ieee.org/document/5397910/
fjournal: IEEE Transactions on Communications
acknowledgement: ack-nhfb
rawauthor: Rong Li and Pooi Yuen Kam and Hua Fu
title:
New representations and bounds for the generalized Marcum $Q$-function via a geometric approach, and an application

rawtitle:
New representations and bounds for the generalized {Marcum} {$Q$}-function via a geometric approach, and an application

entry:
@Article{Li:2010:NRB,
  author =       "Rong Li and Pooi Yuen Kam and Hua Fu",
  title =        "New representations and bounds for the generalized
                 {Marcum} {$Q$}-function via a geometric approach, and
                 an application",
  journal =      j-IEEE-TRANS-COMM,
  volume =       "58",
  number =       "1",
  pages =        "157--169",
  month =        jan,
  year =         "2010",
  CODEN =        "IECMBT",
  DOI =          "https://doi.org/10.1109/tcomm.2010.01.070426",
  ISSN =         "0090-6778 (print), 1558-0857 (electronic)",
  ISSN-L =       "0090-6778",
  bibdate =      "Sat Dec 16 16:52:49 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://ieeexplore.ieee.org/document/5397910/",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Communications",
}


bibtype: article
filename: elefunt.bib
label: Nandagopal:2010:NEF
author: Mohankumar Nandagopal and Soubhadra Sen and Ajay Rawat
title: A Note on the Error Function
journal: j-COMPUT-SCI-ENG
volume: 12
number: 4
pages: 84--88
month: jul
monthnumber: 7
year: 2010
CODEN: CSENFA
DOI: https://doi.org/10.1109/MCSE.2010.79
ISSN: 1521-9615 (print), 1558-366X (electronic) OR 15219615 (print), 1558366X (electronic)
ISSNL: 1521-9615 OR 15219615
bibdate: Tue Jul 27 16:37:11 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.07.27 16:37:11 ???
note: See improvements cite Iacono:2021:BEF.
fjournal: Computing in Science and Engineering
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5992
rawauthor: Mohankumar Nandagopal and Soubhadra Sen and Ajay Rawat
rawnote: See improvements \cite{Iacono:2021:BEF}.
rawtitle: A Note on the Error Function
entry:
@Article{Nandagopal:2010:NEF,
  author =       "Mohankumar Nandagopal and Soubhadra Sen and Ajay
                 Rawat",
  title =        "A Note on the Error Function",
  journal =      j-COMPUT-SCI-ENG,
  volume =       "12",
  number =       "4",
  pages =        "84--88",
  month =        jul # "\slash " # aug,
  year =         "2010",
  CODEN =        "CSENFA",
  DOI =          "https://doi.org/10.1109/MCSE.2010.79",
  ISSN =         "1521-9615 (print), 1558-366X (electronic)",
  ISSN-L =       "1521-9615",
  bibdate =      "Tue Jul 27 16:37:11 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See improvements \cite{Iacono:2021:BEF}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computing in Science and Engineering",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5992",
}


bibtype: article
filename: elefunt.bib
label: Paszkowski:2010:UMC
author: Stefan Paszkowski
title: Untypical methods of convergence acceleration
journal: j-NUMER-ALGORITHMS
volume: 54
pages: ??--??
year: 2010
CODEN: NUALEG
DOI: https://doi.org/10.1007/s11075-010-9381-1
ISSN: 1017-1398 (print), 1572-9265 (electronic) OR 10171398 (print), 15729265 (electronic)
ISSNL: 1017-1398 OR 10171398
bibdate: Mon May 17 14:24:01 MDT 2010
bibtimestamp: 2010.05.17 14:24:01 MDT
URL: http://www.springerlink.com/openurl.asp?genre=article&issn=1017-1398&volume=0&issue=0&spage=??
fjournal: Numerical Algorithms
keywords: convergence acceleration
remark: Article in press, not yet assigned to an issue.
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/11075
rawauthor: Stefan Paszkowski
rawtitle: Untypical methods of convergence acceleration
bibsource:
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1017-1398&volume=0&issue=0; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Paszkowski:2010:UMC,
  author =       "Stefan Paszkowski",
  title =        "Untypical methods of convergence acceleration",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "54",
  number =       "??",
  pages =        "??--??",
  month =        "????",
  year =         "2010",
  CODEN =        "NUALEG",
  DOI =          "https://doi.org/10.1007/s11075-010-9381-1",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Mon May 17 14:24:01 MDT 2010",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1017-1398&volume=0&issue=0;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=1017-1398&volume=0&issue=0&spage=??",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
  keywords =     "convergence acceleration",
  remark =       "Article in press, not yet assigned to an issue.",
}


bibtype: article
filename: elefunt.bib
label: Prevost:2010:RVZ
author: Marc Prevost
title: Recurrence for values of the zeta function
journal: j-APPL-NUM-MATH
volume: 60
number: 12
pages: 1382--1394
month: dec
monthnumber: 12
year: 2010
CODEN: ANMAEL
DOI: https://doi.org/10.1016/j.apnum.2010.05.011
ISSN: 0168-9274 (print), 1873-5460 (electronic) OR 01689274 (print), 18735460 (electronic)
ISSNL: 0168-9274 OR 01689274
bibdate: Sat Oct 16 16:17:49 MDT 2010
bibtimestamp: 2010.10.16 16:17:49 MDT
fjournal: Applied Numerical Mathematics: Transactions of IMACS
keywords: Pade approximants; zeta function
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/01689274/
rawauthor: Marc Pr{\'e}vost
rawtitle: Recurrence for values of the zeta function
abstract:
Using the Pade approximation of the exponential function, we obtain a general recurrence relation for values of the zeta function which contains, as particular cases, many relations already proved. Applications to Bernoulli polynomials are given. Finally, we derive some new recurrence relations with gap of length 4 for zeta numbers.

rawabstract:
Using the Pad{\'e} approximation of the exponential function, we obtain a general recurrence relation for values of the zeta function which contains, as particular cases, many relations already proved. Applications to Bernoulli polynomials are given. Finally, we derive some new recurrence relations with gap of length 4 for zeta numbers.

entry:
@Article{Prevost:2010:RVZ,
  author =       "Marc Pr{\'e}vost",
  title =        "Recurrence for values of the zeta function",
  journal =      j-APPL-NUM-MATH,
  volume =       "60",
  number =       "12",
  pages =        "1382--1394",
  month =        dec,
  year =         "2010",
  CODEN =        "ANMAEL",
  DOI =          "https://doi.org/10.1016/j.apnum.2010.05.011",
  ISSN =         "0168-9274 (print), 1873-5460 (electronic)",
  ISSN-L =       "0168-9274",
  bibdate =      "Sat Oct 16 16:17:49 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applnummath.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "Using the Pad{\'e} approximation of the exponential
                 function, we obtain a general recurrence relation for
                 values of the zeta function which contains, as
                 particular cases, many relations already proved.
                 Applications to Bernoulli polynomials are given.
                 Finally, we derive some new recurrence relations with
                 gap of length 4 for zeta numbers.",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Numerical Mathematics: Transactions of IMACS",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01689274/",
  keywords =     "Pad{\'e} approximants; zeta function",
}


bibtype: article
filename: elefunt.bib
label: Qi:2010:CMS
author: Feng Qi and Senlin Guo and Bai-Ni Guo
title: Complete monotonicity of some functions involving polygamma functions
journal: j-J-COMPUT-APPL-MATH
volume: 233
number: 9
pages: 2149--2160
day: 1
month: mar
monthnumber: 3
year: 2010
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 13:24:22 MST 2017
bibtimestamp: 2017.02.25 13:24:22 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042709006682
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Feng Qi and Senlin Guo and Bai-Ni Guo
rawtitle: Complete monotonicity of some functions involving polygamma functions
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2010.bib

entry:
@Article{Qi:2010:CMS,
  author =       "Feng Qi and Senlin Guo and Bai-Ni Guo",
  title =        "Complete monotonicity of some functions involving
                 polygamma functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "233",
  number =       "9",
  pages =        "2149--2160",
  day =          "1",
  month =        mar,
  year =         "2010",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 13:24:22 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2010.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042709006682",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: article
filename: elefunt.bib
label: Safouhi:2010:BSC
author: Hassan Safouhi
journal: j-NUMER-ALGORITHMS
volume: 54
number: 1
pages: 141--167
month: may
monthnumber: 5
year: 2010
CODEN: NUALEG
ISSN: 1017-1398 (print), 1572-9265 (electronic) OR 10171398 (print), 15729265 (electronic)
ISSNL: 1017-1398 OR 10171398
bibdate: Mon May 17 14:08:57 MDT 2010
bibtimestamp: 2010.05.17 14:08:57 MDT
URL: http://www.springerlink.com/openurl.asp?genre=article&issn=1017-1398&volume=54&issue=1&spage=141
fjournal: Numerical Algorithms
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/11075
rawauthor: Hassan Safouhi
title:
Bessel, sine and cosine functions and extrapolation methods for computing molecular multi-center integrals

bibsource:
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1017-1398&volume=54&issue=1; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

rawtitle:
{Bessel}, sine and cosine functions and extrapolation methods for computing molecular multi-center integrals

entry:
@Article{Safouhi:2010:BSC,
  author =       "Hassan Safouhi",
  title =        "{Bessel}, sine and cosine functions and extrapolation
                 methods for computing molecular multi-center
                 integrals",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "54",
  number =       "1",
  pages =        "141--167",
  month =        may,
  year =         "2010",
  CODEN =        "NUALEG",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Mon May 17 14:08:57 MDT 2010",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1017-1398&volume=54&issue=1;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=1017-1398&volume=54&issue=1&spage=141",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
}


bibtype: article
filename: elefunt.bib
label: Slevinsky:2010:RAT
author: Richard M. Slevinsky and Hassan Safouhi
journal: j-APPL-NUM-MATH
volume: 60
number: 12
pages: 1411--1417
month: dec
monthnumber: 12
year: 2010
CODEN: ANMAEL
DOI: https://doi.org/10.1016/j.apnum.2010.04.005
ISSN: 0168-9274 (print), 1873-5460 (electronic) OR 01689274 (print), 18735460 (electronic)
ISSNL: 0168-9274 OR 01689274
bibdate: Sat Oct 16 16:17:49 MDT 2010
bibtimestamp: 2010.10.16 16:17:49 MDT
fjournal: Applied Numerical Mathematics: Transactions of IMACS
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/01689274/
rawauthor: Richard M. Slevinsky and Hassan Safouhi
title:
A recursive algorithm for the $G$ transformation and accurate computation of incomplete Bessel functions

abstract:
In the present contribution, we develop an efficient algorithm for the recursive computation of the $ G_n^(1) $ source transformation for the approximation of infinite-range integrals. Previous to this contribution, the theoretically powerful $ G_n^(1) $ transformation was handicapped by the lack of an algorithmic implementation. Our proposed algorithm removes this handicap by introducing a recursive computation of the successive $ G_n^(1) $ transformations with respect to the order $n$. This recursion, however, introduces the $ (x^2 d / d x) $ source operator applied to the integrand. Consequently, we employ the Slevinsky--Safouhi formula I for the analytical and numerical developments of these required successive derivatives.par Incomplete Bessel functions, which pose as a numerical challenge, are computed to high pre-determined accuracies using the developed algorithm. The numerical results obtained show the high efficiency of the new method, which does not resort to any numerical integration in the computation.

keywords:
Extrapolation methods; Incomplete Bessel functions; Nonlinear transformations; Slevinsky--Safouhi formulae

rawabstract:
In the present contribution, we develop an efficient algorithm for the recursive computation of the $ G_n^{(1)} $ source transformation for the approximation of infinite-range integrals. Previous to this contribution, the theoretically powerful $ G_n^{(1)} $ transformation was handicapped by the lack of an algorithmic implementation. Our proposed algorithm removes this handicap by introducing a recursive computation of the successive $ G_n^{(1)} $ transformations with respect to the order $n$. This recursion, however, introduces the $ (x^2 d / d x) $ source operator applied to the integrand. Consequently, we employ the Slevinsky--Safouhi formula I for the analytical and numerical developments of these required successive derivatives.\par Incomplete Bessel functions, which pose as a numerical challenge, are computed to high pre-determined accuracies using the developed algorithm. The numerical results obtained show the high efficiency of the new method, which does not resort to any numerical integration in the computation.

rawtitle:
A recursive algorithm for the {$G$} transformation and accurate computation of incomplete {Bessel} functions

entry:
@Article{Slevinsky:2010:RAT,
  author =       "Richard M. Slevinsky and Hassan Safouhi",
  title =        "A recursive algorithm for the {$G$} transformation and
                 accurate computation of incomplete {Bessel} functions",
  journal =      j-APPL-NUM-MATH,
  volume =       "60",
  number =       "12",
  pages =        "1411--1417",
  month =        dec,
  year =         "2010",
  CODEN =        "ANMAEL",
  DOI =          "https://doi.org/10.1016/j.apnum.2010.04.005",
  ISSN =         "0168-9274 (print), 1873-5460 (electronic)",
  ISSN-L =       "0168-9274",
  bibdate =      "Sat Oct 16 16:17:49 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applnummath.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "In the present contribution, we develop an efficient
                 algorithm for the recursive computation of the $
                 G_n^{(1)} $ source transformation for the approximation
                 of infinite-range integrals. Previous to this
                 contribution, the theoretically powerful $ G_n^{(1)} $
                 transformation was handicapped by the lack of an
                 algorithmic implementation. Our proposed algorithm
                 removes this handicap by introducing a recursive
                 computation of the successive $ G_n^{(1)} $
                 transformations with respect to the order $n$. This
                 recursion, however, introduces the $ (x^2 d / d x) $
                 source operator applied to the integrand. Consequently,
                 we employ the Slevinsky--Safouhi formula I for the
                 analytical and numerical developments of these required
                 successive derivatives.\par

                 Incomplete Bessel functions, which pose as a numerical
                 challenge, are computed to high pre-determined
                 accuracies using the developed algorithm. The numerical
                 results obtained show the high efficiency of the new
                 method, which does not resort to any numerical
                 integration in the computation.",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Numerical Mathematics: Transactions of IMACS",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01689274/",
  keywords =     "Extrapolation methods; Incomplete Bessel functions;
                 Nonlinear transformations; Slevinsky--Safouhi
                 formulae",
}


bibtype: inproceedings
filename: elefunt.bib
label: Sofotasios:2010:NEM
author: Paschalis C. Sofotasios and Steven Freear
booktitle: 2010 7th International Symposium on Wireless Communication Systems
title: Novel expressions for the Marcum and one dimensional $Q$-functions
publisher: pub-IEEE
address: pub-IEEE:adr
month: sep
monthnumber: 9
year: 2010
DOI: https://doi.org/10.1109/iswcs.2010.5624374
ISSN: 2154-0217 (print), 2154-0225 (electronic) OR 21540217 (print), 21540225 (electronic)
ISSNL: 2154-0225 OR 21540225
bibdate: Sat Dec 16 17:36:08 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.12.16 17:36:08 ???
URL: http://ieeexplore.ieee.org/document/5624374/
acknowledgement: ack-nhfb
rawauthor: Paschalis C. Sofotasios and Steven Freear
rawbooktitle: 2010 7th International Symposium on Wireless Communication Systems
rawtitle: Novel expressions for the {Marcum} and one dimensional {$Q$}-functions
ISBN:
1-4244-6315-7 (print), 1-4244-6317-3 (e-book), 1-4244-6316-5 (CD-ROM) OR 1424463157 (print), 1424463173 (ebook), 1424463165 (CDROM)

ISBN13:
978-1-4244-6315-2 (print), 978-1-4244-6317-6 (e-book), 978-1-4244-6316-9 (CD-ROM) OR 9781424463152 (print), 9781424463176 (ebook), 9781424463169 (CDROM)

entry:
@InProceedings{Sofotasios:2010:NEM,
  author =       "Paschalis C. Sofotasios and Steven Freear",
  booktitle =    "2010 7th International Symposium on Wireless
                 Communication Systems",
  title =        "Novel expressions for the {Marcum} and one dimensional
                 {$Q$}-functions",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "",
  month =        sep,
  year =         "2010",
  DOI =          "https://doi.org/10.1109/iswcs.2010.5624374",
  ISBN =         "1-4244-6315-7 (print), 1-4244-6317-3 (e-book),
                 1-4244-6316-5 (CD-ROM)",
  ISBN-13 =      "978-1-4244-6315-2 (print), 978-1-4244-6317-6 (e-book),
                 978-1-4244-6316-9 (CD-ROM)",
  ISSN =         "2154-0217 (print), 2154-0225 (electronic)",
  ISSN-L =       "2154-0225",
  bibdate =      "Sat Dec 16 17:36:08 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://ieeexplore.ieee.org/document/5624374/",
  acknowledgement = ack-nhfb,
}


bibtype: book
filename: elefunt.bib
label: Vallee:2010:AFA
author: Olivier Vallee and Manuel Soares
title: Airy Functions and Applications to Physics
publisher: Imperial College Press
address: London WC26 9HE, UK
edition: Second
pages: x + 202
year: 2010
ISBN: 1-84816-548-X, 1-84816-550-1 OR 184816548X, 1848165501
ISBN13: 978-1-84816-548-9, 978-1-84816-550-2 OR 9781848165489, 9781848165502
LCCN: QA351
bibdate: Tue Dec 5 10:05:10 MST 2023
bibsource: fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2023.12.05 10:05:10 MST
remark: See also first edition cite Vallee:2004:AFA
subject: Airy functions; Airy-Funktion; Mathematische Physik
acknowledgement: ack-nhfb
rawauthor: Olivier Vall{\'e}e and Manuel Soares
rawtitle: {Airy} Functions and Applications to Physics
abstract:
Addressed mainly to physicist and chemical physicist, this textbook is the result of a broad compilation of current knowledge on analytical properties of Airy functions. In particular, the calculus implying the Airy functions is developed with care. In the latter chapters, examples are given to succinctly illustrate the use of Airy functions in classical and quantum physics. The physicist, for instance in fluid mechanics, can find what he is looking for, in the references for works of molecular physics or in physics of surfaces, and vice versa. The knowledge on Airy functions is frequently reviewed. The reason may be found in the need to express a physical phenomenon in terms of an effective and comprehensive analytical form for the whole scientific community.

TOC:
Preface / x 1: A Historical Introduction: Sir George Biddell Airy / 1 2: Definitions and Properties / 5 2.1: Homogeneous Airy functions 2.1.1: The Airy equation 2.1.2: Elementary properties 2.1.3: Integral representations 2.1.4: Ascending and asymptotic series 2.2: Properties of Airy functions 2.2.1: Zeros of Airy functions 2.2.2: The spectral zeta function 2.2.3: Inequalities 2.2.4: Connection with Bessel functions 2.2.5: Modulus and phase of Airy functions 2.3: Inhomogeneous Airy functions 2.3.1: Definitions 2.3.2: Properties of inhomogeneous Airy functions 2.3.3: Ascending series and asymptotic expansion 2.3.4: Zeros of the Scorer functions 2.4: Squares and products of Airy functions 2.4.1: Differential equation and integral representation 2.4.2: A remarkable identity 2.4.3: The product $Ai (x) Ai (-x)$: Airy wavelets 3: Primitives and Integrals of Airy Functions / 37 3.1: Primitives containing one Airy function 3.1.1: In terms of Airy functions 3.1.2: Ascending series 3.1.3: Asymptotic expansions 3.1.4: Primitives of Scorer functions 3.1.5: Repeated primitives 3.2: Product of Airy functions 3.2.1: The method of Albright 3.2.2: Some primitives 3.3: Other primitives 3.4: Miscellaneous 3.5: Elementary integrals 3.5.1: Particular integrals 3.5.2: Integrals containing a single Airy function 3.5.3: Integrals of products of two Airy functions 3.6: Other integrals 3.6.1: Integrals involving the Volterra $mu $-function 3.6.2: Canonisation of cubic forms 3.6.3: Integrals with three Airy functions 3.6.4: Integrals with four Airy functions 3.6.5: Double integrals 4: Transformations of Airy functions / 69 4.1: Causal properties of Airy functions 4.1.1: Causal relations 4.1.2: Green's function of the Airy equation 4.1.3: Fractional derivatives of Airy functions 4.2: The Airy transform 4.2.1: Definitions and elementary properties 4.2.2: Some examples 4.2.3: Airy polynomials 4.2.4: A particular case: correlation Airy transform 4.3: Other kinds of transformations 4.3.1: Laplace transform of Airy functions 4.3.2: Mellin transform of Airy functions 4.3.3: Fourier transform of Airy functions 4.3.4: Hankel transform and the Airy kernel 4.4: Expansion into Fourier--Airy series 5: The Uniform Approximation / 101 5.1: Oscillating integrals 5.1.1: The method of stationary phase 5.1.2: The uniform approximation of oscillating integrals 5.1.3: The Airy uniform approximation 5.2: Differential equations of the second order 5.2.1: The JWKB method 5.2.2: The Langer generalisation 5.3: Inhomogeneous differential equations 6: Generalisation of Airy Functions / 111 6.1: Generalisation of the Airy integral 6.1.1: The generalisation of Watson 6.1.2: Oscillating integrals and catastrophes 6.2: Third order differential equations 6.2.1: The linear third order differential equation 6.2.2: Asymptotic solutions 6.2.3: The comparison equation 6.3: A differential equation of the fourth order 7: Applications to Classical Physics / 127 7.1: Optics and electromagnetism 7.2: Fluid mechanics 7.2.1: The Tricomi equation 7.2.2: The Orr--Sommerfeld equation 7.3: Elasticity 7.4: The heat equation 7.5: Nonlinear physics 7.5.1: Korteweg--de Vries equation 7.5.2: The Second Painleve equation 8: Applications to Quantum Physics / 147 8.1: The Schrodinger equation 8.1.1: Particle in a Uniform field 8.1.2: The 8.1.3: Uniform approximation of the Schrodinger equation 8.2: Evaluation of the Franck--Condon factors 8.2.1: The Franck--Condon principle 8.2.2: The JWKB approximation 8.2.3: The uniform approximation 8.3: The semiclassical Wigner distribution 8.3.1: The Weyl--Wigner formalism 8.3.2: The one-dimensional Wigner distribution 8.3.3: The two-dimensional Wigner distribution 8.3.4: Configuration of the Wigner distribution 8.4: Airy transform of the Schrodinger equation Appendix A: Numerical Computation of the Airy Functions / 185 A.1: Homogeneous functions A.2: Inhomogeneous functions Bibliography / 191 Index / 201

rawabstract:
Addressed mainly to physicist and chemical physicist, this textbook is the result of a broad compilation of current knowledge on analytical properties of Airy functions. In particular, the calculus implying the Airy functions is developed with care. In the latter chapters, examples are given to succinctly illustrate the use of Airy functions in classical and quantum physics. The physicist, for instance in fluid mechanics, can find what he is looking for, in the references for works of molecular physics or in physics of surfaces, and vice versa. The knowledge on Airy functions is frequently reviewed. The reason may be found in the need to express a physical phenomenon in terms of an effective and comprehensive analytical form for the whole scientific community.

rawTOC:
Preface / x \\ 1: A Historical Introduction: Sir George Biddell Airy / 1 \\ 2: Definitions and Properties / 5 \\ 2.1: Homogeneous Airy functions \\ 2.1.1: The Airy equation \\ 2.1.2: Elementary properties \\ 2.1.3: Integral representations \\ 2.1.4: Ascending and asymptotic series \\ 2.2: Properties of Airy functions \\ 2.2.1: Zeros of Airy functions \\ 2.2.2: The spectral zeta function \\ 2.2.3: Inequalities \\ 2.2.4: Connection with Bessel functions \\ 2.2.5: Modulus and phase of Airy functions \\ 2.3: Inhomogeneous Airy functions \\ 2.3.1: Definitions \\ 2.3.2: Properties of inhomogeneous Airy functions \\ 2.3.3: Ascending series and asymptotic expansion \\ 2.3.4: Zeros of the Scorer functions \\ 2.4: Squares and products of Airy functions \\ 2.4.1: Differential equation and integral representation \\ 2.4.2: A remarkable identity \\ 2.4.3: The product $\Ai(x) \Ai(-x)$: Airy wavelets \\ 3: Primitives and Integrals of Airy Functions / 37 \\ 3.1: Primitives containing one Airy function \\ 3.1.1: In terms of Airy functions \\ 3.1.2: Ascending series \\ 3.1.3: Asymptotic expansions \\ 3.1.4: Primitives of Scorer functions \\ 3.1.5: Repeated primitives \\ 3.2: Product of Airy functions \\ 3.2.1: The method of Albright \\ 3.2.2: Some primitives \\ 3.3: Other primitives \\ 3.4: Miscellaneous \\ 3.5: Elementary integrals \\ 3.5.1: Particular integrals \\ 3.5.2: Integrals containing a single Airy function \\ 3.5.3: Integrals of products of two Airy functions \\ 3.6: Other integrals \\ 3.6.1: Integrals involving the Volterra $\mu$-function \\ 3.6.2: Canonisation of cubic forms \\ 3.6.3: Integrals with three Airy functions \\ 3.6.4: Integrals with four Airy functions \\ 3.6.5: Double integrals \\ 4: Transformations of Airy functions / 69 \\ 4.1: Causal properties of Airy functions \\ 4.1.1: Causal relations \\ 4.1.2: Green's function of the Airy equation \\ 4.1.3: Fractional derivatives of Airy functions \\ 4.2: The Airy transform \\ 4.2.1: Definitions and elementary properties \\ 4.2.2: Some examples \\ 4.2.3: Airy polynomials \\ 4.2.4: A particular case: correlation Airy transform \\ 4.3: Other kinds of transformations \\ 4.3.1: Laplace transform of Airy functions \\ 4.3.2: Mellin transform of Airy functions \\ 4.3.3: Fourier transform of Airy functions \\ 4.3.4: Hankel transform and the Airy kernel \\ 4.4: Expansion into Fourier--Airy series \\ 5: The Uniform Approximation / 101 \\ 5.1: Oscillating integrals \\ 5.1.1: The method of stationary phase \\ 5.1.2: The uniform approximation of oscillating integrals \\ 5.1.3: The Airy uniform approximation \\ 5.2: Differential equations of the second order \\ 5.2.1: The JWKB method \\ 5.2.2: The Langer generalisation \\ 5.3: Inhomogeneous differential equations \\ 6: Generalisation of Airy Functions / 111 \\ 6.1: Generalisation of the Airy integral \\ 6.1.1: The generalisation of Watson \\ 6.1.2: Oscillating integrals and catastrophes \\ 6.2: Third order differential equations \\ 6.2.1: The linear third order differential equation \\ 6.2.2: Asymptotic solutions \\ 6.2.3: The comparison equation \\ 6.3: A differential equation of the fourth order \\ 7: Applications to Classical Physics / 127 \\ 7.1: Optics and electromagnetism \\ 7.2: Fluid mechanics \\ 7.2.1: The Tricomi equation \\ 7.2.2: The Orr--Sommerfeld equation \\ 7.3: Elasticity \\ 7.4: The heat equation \\ 7.5: Nonlinear physics \\ 7.5.1: Korteweg--de Vries equation \\ 7.5.2: The Second Painlev{\'e} equation \\ 8: Applications to Quantum Physics / 147 \\ 8.1: The Schr{\"o}dinger equation \\ 8.1.1: Particle in a Uniform field \\ 8.1.2: The 8.1.3: Uniform approximation of the Schr{\"o}dinger equation \\ 8.2: Evaluation of the Franck--Condon factors \\ 8.2.1: The Franck--Condon principle \\ 8.2.2: The JWKB approximation \\ 8.2.3: The uniform approximation \\ 8.3: The semiclassical Wigner distribution \\ 8.3.1: The Weyl--Wigner formalism \\ 8.3.2: The one-dimensional Wigner distribution \\ 8.3.3: The two-dimensional Wigner distribution \\ 8.3.4: Configuration of the Wigner distribution \\ 8.4: Airy transform of the Schr{\"o}dinger equation \\ Appendix A: Numerical Computation of the Airy Functions / 185 \\ A.1: Homogeneous functions \\ A.2: Inhomogeneous functions \\ Bibliography / 191 \\ Index / 201

entry:
@Book{Vallee:2010:AFA,
  author =       "Olivier Vall{\'e}e and Manuel Soares",
  title =        "{Airy} Functions and Applications to Physics",
  publisher =    "Imperial College Press",
  address =      "London WC26 9HE, UK",
  edition =      "Second",
  pages =        "x + 202",
  year =         "2010",
  ISBN =         "1-84816-548-X, 1-84816-550-1",
  ISBN-13 =      "978-1-84816-548-9, 978-1-84816-550-2",
  LCCN =         "QA351",
  bibdate =      "Tue Dec 5 10:05:10 MST 2023",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "Addressed mainly to physicist and chemical physicist,
                 this textbook is the result of a broad compilation of
                 current knowledge on analytical properties of Airy
                 functions. In particular, the calculus implying the
                 Airy functions is developed with care. In the latter
                 chapters, examples are given to succinctly illustrate
                 the use of Airy functions in classical and quantum
                 physics. The physicist, for instance in fluid
                 mechanics, can find what he is looking for, in the
                 references for works of molecular physics or in physics
                 of surfaces, and vice versa. The knowledge on Airy
                 functions is frequently reviewed. The reason may be
                 found in the need to express a physical phenomenon in
                 terms of an effective and comprehensive analytical form
                 for the whole scientific community.",
  acknowledgement = ack-nhfb,
  remark =       "See also first edition \cite{Vallee:2004:AFA}",
  subject =      "Airy functions; Airy-Funktion; Mathematische Physik",
  tableofcontents = "Preface / x \\
                 1: A Historical Introduction: Sir George Biddell Airy /
                 1 \\
                 2: Definitions and Properties / 5 \\
                 2.1: Homogeneous Airy functions \\
                 2.1.1: The Airy equation \\
                 2.1.2: Elementary properties \\
                 2.1.3: Integral representations \\
                 2.1.4: Ascending and asymptotic series \\
                 2.2: Properties of Airy functions \\
                 2.2.1: Zeros of Airy functions \\
                 2.2.2: The spectral zeta function \\
                 2.2.3: Inequalities \\
                 2.2.4: Connection with Bessel functions \\
                 2.2.5: Modulus and phase of Airy functions \\
                 2.3: Inhomogeneous Airy functions \\
                 2.3.1: Definitions \\
                 2.3.2: Properties of inhomogeneous Airy functions \\
                 2.3.3: Ascending series and asymptotic expansion \\
                 2.3.4: Zeros of the Scorer functions \\
                 2.4: Squares and products of Airy functions \\
                 2.4.1: Differential equation and integral
                 representation \\
                 2.4.2: A remarkable identity \\
                 2.4.3: The product $\Ai(x) \Ai(-x)$: Airy wavelets \\
                 3: Primitives and Integrals of Airy Functions / 37 \\
                 3.1: Primitives containing one Airy function \\
                 3.1.1: In terms of Airy functions \\
                 3.1.2: Ascending series \\
                 3.1.3: Asymptotic expansions \\
                 3.1.4: Primitives of Scorer functions \\
                 3.1.5: Repeated primitives \\
                 3.2: Product of Airy functions \\
                 3.2.1: The method of Albright \\
                 3.2.2: Some primitives \\
                 3.3: Other primitives \\
                 3.4: Miscellaneous \\
                 3.5: Elementary integrals \\
                 3.5.1: Particular integrals \\
                 3.5.2: Integrals containing a single Airy function \\
                 3.5.3: Integrals of products of two Airy functions \\
                 3.6: Other integrals \\
                 3.6.1: Integrals involving the Volterra $\mu$-function
                 \\
                 3.6.2: Canonisation of cubic forms \\
                 3.6.3: Integrals with three Airy functions \\
                 3.6.4: Integrals with four Airy functions \\
                 3.6.5: Double integrals \\
                 4: Transformations of Airy functions / 69 \\
                 4.1: Causal properties of Airy functions \\
                 4.1.1: Causal relations \\
                 4.1.2: Green's function of the Airy equation \\
                 4.1.3: Fractional derivatives of Airy functions \\
                 4.2: The Airy transform \\
                 4.2.1: Definitions and elementary properties \\
                 4.2.2: Some examples \\
                 4.2.3: Airy polynomials \\
                 4.2.4: A particular case: correlation Airy transform
                 \\
                 4.3: Other kinds of transformations \\
                 4.3.1: Laplace transform of Airy functions \\
                 4.3.2: Mellin transform of Airy functions \\
                 4.3.3: Fourier transform of Airy functions \\
                 4.3.4: Hankel transform and the Airy kernel \\
                 4.4: Expansion into Fourier--Airy series \\
                 5: The Uniform Approximation / 101 \\
                 5.1: Oscillating integrals \\
                 5.1.1: The method of stationary phase \\
                 5.1.2: The uniform approximation of oscillating
                 integrals \\
                 5.1.3: The Airy uniform approximation \\
                 5.2: Differential equations of the second order \\
                 5.2.1: The JWKB method \\
                 5.2.2: The Langer generalisation \\
                 5.3: Inhomogeneous differential equations \\
                 6: Generalisation of Airy Functions / 111 \\
                 6.1: Generalisation of the Airy integral \\
                 6.1.1: The generalisation of Watson \\
                 6.1.2: Oscillating integrals and catastrophes \\
                 6.2: Third order differential equations \\
                 6.2.1: The linear third order differential equation \\
                 6.2.2: Asymptotic solutions \\
                 6.2.3: The comparison equation \\
                 6.3: A differential equation of the fourth order \\
                 7: Applications to Classical Physics / 127 \\
                 7.1: Optics and electromagnetism \\
                 7.2: Fluid mechanics \\
                 7.2.1: The Tricomi equation \\
                 7.2.2: The Orr--Sommerfeld equation \\
                 7.3: Elasticity \\
                 7.4: The heat equation \\
                 7.5: Nonlinear physics \\
                 7.5.1: Korteweg--de Vries equation \\
                 7.5.2: The Second Painlev{\'e} equation \\
                 8: Applications to Quantum Physics / 147 \\
                 8.1: The Schr{\"o}dinger equation \\
                 8.1.1: Particle in a Uniform field \\
                 8.1.2: The 8.1.3: Uniform approximation of the
                 Schr{\"o}dinger equation \\
                 8.2: Evaluation of the Franck--Condon factors \\
                 8.2.1: The Franck--Condon principle \\
                 8.2.2: The JWKB approximation \\
                 8.2.3: The uniform approximation \\
                 8.3: The semiclassical Wigner distribution \\
                 8.3.1: The Weyl--Wigner formalism \\
                 8.3.2: The one-dimensional Wigner distribution \\
                 8.3.3: The two-dimensional Wigner distribution \\
                 8.3.4: Configuration of the Wigner distribution \\
                 8.4: Airy transform of the Schr{\"o}dinger equation \\
                 Appendix A: Numerical Computation of the Airy Functions
                 / 185 \\
                 A.1: Homogeneous functions \\
                 A.2: Inhomogeneous functions \\
                 Bibliography / 191 \\
                 Index / 201",
}


bibtype: article
filename: elefunt.bib
label: Weniger:2010:SDP
author: E. J. Weniger
title: Summation of divergent power series by means of factorial series
journal: j-APPL-NUM-MATH
volume: 60
number: 12
pages: 1429--1441
year: 2010
CODEN: ANMAEL
ISSN: 0168-9274 (print), 1873-5460 (electronic) OR 01689274 (print), 18735460 (electronic)
ISSNL: 0168-9274 OR 01689274
bibdate: Thu Dec 01 10:37:55 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2011.12.01 10:37:55 ???
fjournal: Applied Numerical Mathematics: Transactions of IMACS
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/01689274/
rawauthor: E. J. Weniger
rawtitle: Summation of divergent power series by means of factorial series
note:
Presented at Approximation and Extrapolation of Convergent and Divergent Sequences and Series (CIRM, Luminy --- France, 2009).

rawnote:
Presented at Approximation and Extrapolation of Convergent and Divergent Sequences and Series (CIRM, Luminy --- France, 2009).

entry:
@Article{Weniger:2010:SDP,
  author =       "E. J. Weniger",
  title =        "Summation of divergent power series by means of
                 factorial series",
  journal =      j-APPL-NUM-MATH,
  volume =       "60",
  number =       "12",
  pages =        "1429--1441",
  month =        "????",
  year =         "2010",
  CODEN =        "ANMAEL",
  ISSN =         "0168-9274 (print), 1873-5460 (electronic)",
  ISSN-L =       "0168-9274",
  bibdate =      "Thu Dec 01 10:37:55 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Presented at Approximation and Extrapolation of
                 Convergent and Divergent Sequences and Series (CIRM,
                 Luminy --- France, 2009).",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Numerical Mathematics: Transactions of IMACS",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01689274/",
}


bibtype: article
filename: elefunt.bib
label: Wozny:2010:EAS
author: Pawel Wozny
title: Efficient algorithm for summation of some slowly convergent series
journal: j-APPL-NUM-MATH
volume: 60
number: 12
pages: 1442--1453
year: 2010
CODEN: ANMAEL
ISSN: 0168-9274 (print), 1873-5460 (electronic) OR 01689274 (print), 18735460 (electronic)
ISSNL: 0168-9274 OR 01689274
bibdate: Thu Dec 01 09:26:24 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2011.12.01 09:26:24 ???
fjournal: Applied Numerical Mathematics: Transactions of IMACS
keywords: convergence acceleration
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/01689274/
rawauthor: Pawe{\l} Wo{\'z}ny
rawtitle: Efficient algorithm for summation of some slowly convergent series
note:
Presented at Approximation and Extrapolation of Convergent and Divergent Sequences and Series (CIRM, Luminy - France, 2009).

rawnote:
Presented at Approximation and Extrapolation of Convergent and Divergent Sequences and Series (CIRM, Luminy - France, 2009).

entry:
@Article{Wozny:2010:EAS,
  author =       "Pawe{\l} Wo{\'z}ny",
  title =        "Efficient algorithm for summation of some slowly
                 convergent series",
  journal =      j-APPL-NUM-MATH,
  volume =       "60",
  number =       "12",
  pages =        "1442--1453",
  month =        "????",
  year =         "2010",
  CODEN =        "ANMAEL",
  ISSN =         "0168-9274 (print), 1873-5460 (electronic)",
  ISSN-L =       "0168-9274",
  bibdate =      "Thu Dec 01 09:26:24 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Presented at Approximation and Extrapolation of
                 Convergent and Divergent Sequences and Series (CIRM,
                 Luminy - France, 2009).",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Numerical Mathematics: Transactions of IMACS",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01689274/",
  keywords =     "convergence acceleration",
}


bibtype: article
filename: elefunt.bib
label: Zhu:2010:JTI
author: Ling Zhu
title: Jordan type inequalities involving the Bessel and modified Bessel functions
journal: j-COMPUT-MATH-APPL
volume: 59
number: 2
pages: 724--736
month: jan
monthnumber: 1
year: 2010
CODEN: CMAPDK
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Wed Mar 1 21:50:34 MST 2017
bibtimestamp: 2017.03.01 21:50:34 MST
URL: http://www.sciencedirect.com/science/article/pii/S0898122109007196
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/08981221
rawauthor: Ling Zhu
rawtitle: {Jordan} type inequalities involving the {Bessel} and modified {Bessel} functions
bibsource:
https://www.math.utah.edu/pub/tex/bib/computmathappl2010.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Zhu:2010:JTI,
  author =       "Ling Zhu",
  title =        "{Jordan} type inequalities involving the {Bessel} and
                 modified {Bessel} functions",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "59",
  number =       "2",
  pages =        "724--736",
  month =        jan,
  year =         "2010",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 21:50:34 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0898122109007196",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}


bibtype: article
filename: elefunt.bib
label: Ali:2011:NGJ
author: Ahmad T. Ali
title: New generalized Jacobi elliptic function rational expansion method
journal: j-J-COMPUT-APPL-MATH
volume: 235
number: 14
pages: 4117--4127
day: 15
month: may
monthnumber: 5
year: 2011
CODEN: JCAMDI
DOI: https://doi.org/10.1016/j.cam.2011.03.002
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 13:24:28 MST 2017
bibtimestamp: 2017.02.25 13:24:28 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042711001257
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Ahmad T. Ali
rawtitle: New generalized {Jacobi} elliptic function rational expansion method
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2010.bib

entry:
@Article{Ali:2011:NGJ,
  author =       "Ahmad T. Ali",
  title =        "New generalized {Jacobi} elliptic function rational
                 expansion method",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "235",
  number =       "14",
  pages =        "4117--4127",
  day =          "15",
  month =        may,
  year =         "2011",
  CODEN =        "JCAMDI",
  DOI =          "https://doi.org/10.1016/j.cam.2011.03.002",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 13:24:28 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2010.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042711001257",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: inproceedings
filename: elefunt.bib
label: Borwein:2011:SVG
author: Jonathan M. Borwein and Armin Straub
title: Special values of generalized log-sine integrals
crossref: Schost:2011:IPI
pages: 43--50
year: 2011
DOI: https://doi.org/10.1145/1993886.1993899
bibdate: Fri Mar 14 12:20:08 MDT 2014
bibtimestamp: 2014.03.14 12:20:08 MDT
acknowledgement: ack-nhfb
rawauthor: Jonathan M. Borwein and Armin Straub
rawtitle: Special values of generalized log-sine integrals
bibsource:
http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/issac.bib; https://www.math.utah.edu/pub/tex/bib/mathematica.bib

abstract:
We study generalized log-sine integrals at special values. At $ pi $ and multiples thereof explicit evaluations are obtained in terms of Nielsen polylogarithms at $ pm 1 $. For general arguments we present algorithmic evaluations involving Nielsen polylogarithms at related arguments. In particular, we consider log-sine integrals at $ pi / 3 $ which evaluate in terms of polylogarithms at the sixth root of unity. An implementation of our results for the computer algebra systems Mathematica and SAGE is provided.

rawabstract:
We study generalized log-sine integrals at special values. At $ \pi $ and multiples thereof explicit evaluations are obtained in terms of Nielsen polylogarithms at $ \pm 1 $. For general arguments we present algorithmic evaluations involving Nielsen polylogarithms at related arguments. In particular, we consider log-sine integrals at $ \pi / 3 $ which evaluate in terms of polylogarithms at the sixth root of unity. An implementation of our results for the computer algebra systems Mathematica and SAGE is provided.

entry:
@InProceedings{Borwein:2011:SVG,
  author =       "Jonathan M. Borwein and Armin Straub",
  title =        "Special values of generalized log-sine integrals",
  crossref =     "Schost:2011:IPI",
  pages =        "43--50",
  year =         "2011",
  DOI =          "https://doi.org/10.1145/1993886.1993899",
  bibdate =      "Fri Mar 14 12:20:08 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/issac.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathematica.bib",
  abstract =     "We study generalized log-sine integrals at special
                 values. At $ \pi $ and multiples thereof explicit
                 evaluations are obtained in terms of Nielsen
                 polylogarithms at $ \pm 1 $. For general arguments we
                 present algorithmic evaluations involving Nielsen
                 polylogarithms at related arguments. In particular, we
                 consider log-sine integrals at $ \pi / 3 $ which
                 evaluate in terms of polylogarithms at the sixth root
                 of unity. An implementation of our results for the
                 computer algebra systems Mathematica and SAGE is
                 provided.",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: elefunt.bib
label: Brisebarre:2011:APS
crossref: Schwarz:2011:PIS
pages: 23--30
year: 2011
DOI: https://doi.org/10.1109/ARITH.2011.13
bibdate: Sat Aug 20 09:00:00 MDT 2011
bibtimestamp: 2011.08.20 09:00:00 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992105
keywords: ARITH-20; hypotenuse
acknowledgement: ack-nhfb
author:
Nicolas Brisebarre and Mioara Joldes and Peter Kornerup and Erik Martin-Dorel and Jean-Michel Muller

title:
Augmented Precision Square Roots and $2$-D Norms, and Discussion on Correctly Rounding $ sqrt x^2 + y^2 $

rawauthor:
Nicolas Brisebarre and Mioara Joldes and Peter Kornerup and {\'E}rik Martin-Dorel and Jean-Michel Muller

rawtitle:
Augmented Precision Square Roots and {$2$-D} Norms, and Discussion on Correctly Rounding $ \sqrt {x^2 + y^2} $

entry:
@InProceedings{Brisebarre:2011:APS,
  author =       "Nicolas Brisebarre and Mioara Joldes and Peter
                 Kornerup and {\'E}rik Martin-Dorel and Jean-Michel
                 Muller",
  title =        "Augmented Precision Square Roots and {$2$-D} Norms,
                 and Discussion on Correctly Rounding $ \sqrt {x^2 +
                 y^2} $",
  crossref =     "Schwarz:2011:PIS",
  pages =        "23--30",
  year =         "2011",
  DOI =          "https://doi.org/10.1109/ARITH.2011.13",
  bibdate =      "Sat Aug 20 09:00:00 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992105",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-20; hypotenuse",
}


bibtype: inproceedings
filename: elefunt.bib
label: Butts:2011:RDR
author: J. Adam Butts and Ping Tak Peter Tang and Ron O. Dror and David E. Shaw
crossref: Schwarz:2011:PIS
pages: 149--158
year: 2011
DOI: https://doi.org/10.1109/ARITH.2011.28
bibdate: Sat Aug 20 09:00:00 MDT 2011
bibtimestamp: 2011.08.20 09:00:00 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992120
keywords: ARITH-20
acknowledgement: ack-nhfb
rawauthor: J. Adam Butts and Ping Tak Peter Tang and Ron O. Dror and David E. Shaw
title:
Radix-8 Digit-by-Rounding: Achieving High-Performance Reciprocals, Square Roots, and Reciprocal Square Roots

rawtitle:
Radix-8 Digit-by-Rounding: Achieving High-Performance Reciprocals, Square Roots, and Reciprocal Square Roots

entry:
@InProceedings{Butts:2011:RDR,
  author =       "J. Adam Butts and Ping Tak Peter Tang and Ron O. Dror
                 and David E. Shaw",
  title =        "Radix-8 Digit-by-Rounding: Achieving High-Performance
                 Reciprocals, Square Roots, and Reciprocal Square
                 Roots",
  crossref =     "Schwarz:2011:PIS",
  pages =        "149--158",
  year =         "2011",
  DOI =          "https://doi.org/10.1109/ARITH.2011.28",
  bibdate =      "Sat Aug 20 09:00:00 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992120",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-20",
}


bibtype: article
filename: elefunt.bib
label: Cai:2011:CSB
author: Liang-Wu Cai
title: On the computation of spherical Bessel functions of complex arguments
journal: j-COMP-PHYS-COMM
volume: 182
number: 3
pages: 663--668
month: mar
monthnumber: 3
year: 2011
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/j.cpc.2010.11.019
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Sat Feb 11 10:10:56 MST 2012
bibtimestamp: 2012.02.11 10:10:56 MST
URL: http://www.sciencedirect.com/science/article/pii/S0010465510004650
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: Liang-Wu Cai
rawtitle: On the computation of spherical {Bessel} functions of complex arguments
bibsource:
https://www.math.utah.edu/pub/tex/bib/compphyscomm2010.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Cai:2011:CSB,
  author =       "Liang-Wu Cai",
  title =        "On the computation of spherical {Bessel} functions of
                 complex arguments",
  journal =      j-COMP-PHYS-COMM,
  volume =       "182",
  number =       "3",
  pages =        "663--668",
  month =        mar,
  year =         "2011",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/j.cpc.2010.11.019",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Sat Feb 11 10:10:56 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465510004650",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}


bibtype: article
filename: elefunt.bib
label: Cardoso:2011:IFP
author: Joao Ribeiro Cardoso and Ana F. Loureiro
title: Iteration functions for $p$ th roots of complex numbers
journal: j-NUMER-ALGORITHMS
volume: 57
number: 3
pages: 329--356
month: jul
monthnumber: 7
year: 2011
CODEN: NUALEG
ISSN: 1017-1398 (print), 1572-9265 (electronic) OR 10171398 (print), 15729265 (electronic)
ISSNL: 1017-1398 OR 10171398
bibdate: Fri Jul 22 09:48:58 MDT 2011
bibtimestamp: 2011.07.22 09:48:58 MDT
URL: http://www.springerlink.com/openurl.asp?genre=article&issn=1017-1398&volume=57&issue=3&spage=329
fjournal: Numerical Algorithms
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/11075
rawauthor: Jo{\~a}o Ribeiro Cardoso and Ana F. Loureiro
rawtitle: Iteration functions for $p$ th roots of complex numbers
bibsource:
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1017-1398&volume=57&issue=3; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

abstract:
A novel way of generating higher-order iteration functions for the computation of pth roots of complex numbers is the main contribution of the present work. The behavior of some of these iteration functions will be analyzed and the conditions on the starting values that guarantee the convergence will be stated. The illustration of the basins of attractions of the pth roots will be carried out by some computer generated plots. In order to compare the performance of the iterations some numerical examples will be considered.

rawabstract:
A novel way of generating higher-order iteration functions for the computation of pth roots of complex numbers is the main contribution of the present work. The behavior of some of these iteration functions will be analyzed and the conditions on the starting values that guarantee the convergence will be stated. The illustration of the basins of attractions of the pth roots will be carried out by some computer generated plots. In order to compare the performance of the iterations some numerical examples will be considered.

entry:
@Article{Cardoso:2011:IFP,
  author =       "Jo{\~a}o Ribeiro Cardoso and Ana F. Loureiro",
  title =        "Iteration functions for $p$ th roots of complex
                 numbers",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "57",
  number =       "3",
  pages =        "329--356",
  month =        jul,
  year =         "2011",
  CODEN =        "NUALEG",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Fri Jul 22 09:48:58 MDT 2011",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1017-1398&volume=57&issue=3;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=1017-1398&volume=57&issue=3&spage=329",
  abstract =     "A novel way of generating higher-order iteration
                 functions for the computation of pth roots of complex
                 numbers is the main contribution of the present work.
                 The behavior of some of these iteration functions will
                 be analyzed and the conditions on the starting values
                 that guarantee the convergence will be stated. The
                 illustration of the basins of attractions of the pth
                 roots will be carried out by some computer generated
                 plots. In order to compare the performance of the
                 iterations some numerical examples will be
                 considered.",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
}


bibtype: article
filename: elefunt.bib
label: Chang:2011:CTB
author: Seok-Ho Chang and Pamela C. Cosman and Laurence B. Milstein
title: Chernoff-Type Bounds for the Gaussian Error Function
journal: j-IEEE-TRANS-COMM
volume: 59
number: 11
pages: 2939--2944
month: nov
monthnumber: 11
year: 2011
CODEN: IECMBT
DOI: https://doi.org/10.1109/tcomm.2011.072011.100049
ISSN: 0090-6778 (print), 1558-0857 (electronic) OR 00906778 (print), 15580857 (electronic)
ISSNL: 0090-6778 OR 00906778
bibdate: Fri Jul 22 09:48:58 MDT 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2011.07.22 09:48:58 MDT
fjournal: IEEE Transactions on Communications
acknowledgement: ack-nhfb
rawauthor: Seok-Ho Chang and Pamela C. Cosman and Laurence B. Milstein
rawtitle: {Chernoff}-Type Bounds for the {Gaussian} Error Function
entry:
@Article{Chang:2011:CTB,
  author =       "Seok-Ho Chang and Pamela C. Cosman and Laurence B.
                 Milstein",
  title =        "{Chernoff}-Type Bounds for the {Gaussian} Error
                 Function",
  journal =      j-IEEE-TRANS-COMM,
  volume =       "59",
  number =       "11",
  pages =        "2939--2944",
  month =        nov,
  year =         "2011",
  CODEN =        "IECMBT",
  DOI =          "https://doi.org/10.1109/tcomm.2011.072011.100049",
  ISSN =         "0090-6778 (print), 1558-0857 (electronic)",
  ISSN-L =       "0090-6778",
  bibdate =      "Fri Jul 22 09:48:58 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Communications",
}


bibtype: article
filename: elefunt.bib
label: Chen:2011:SPF
author: Chao-Ping Chen
title: Some properties of functions related to the gamma, psi and tetragamma functions
journal: j-COMPUT-MATH-APPL
volume: 62
number: 9
pages: 3389--3395
month: nov
monthnumber: 11
year: 2011
CODEN: CMAPDK
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Wed Mar 1 21:51:02 MST 2017
bibtimestamp: 2017.03.01 21:51:02 MST
URL: http://www.sciencedirect.com/science/article/pii/S0898122111007267
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/08981221
rawauthor: Chao-Ping Chen
rawtitle: Some properties of functions related to the gamma, psi and tetragamma functions
bibsource:
https://www.math.utah.edu/pub/tex/bib/computmathappl2010.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Chen:2011:SPF,
  author =       "Chao-Ping Chen",
  title =        "Some properties of functions related to the gamma, psi
                 and tetragamma functions",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "62",
  number =       "9",
  pages =        "3389--3395",
  month =        nov,
  year =         "2011",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 21:51:02 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0898122111007267",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}


bibtype: inproceedings
filename: elefunt.bib
label: Chen:2011:TSA
author: Jianxun Chen and Yongzhong Huang and Shaozhong Guo and Shimiao Chen and Wei Wang
booktitle: 2011 Third International Conference on Measuring Technology and Mechatronics Automation (ICMTMA)
title: Test Standardization and Analyse Model of Mathematical Functions for Precision
volume: 3
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 652--655
year: 2011
DOI: https://doi.org/10.1109/ICMTMA.2011.734
ISBN: 0-7695-4296-4 OR 0769542964
ISBN13: 978-0-7695-4296-6 OR 9780769542966
bibdate: Tue Sep 27 08:11:02 MDT 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2011.09.27 08:11:02 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5721571
acknowledgement: ack-nhfb
bookURL: http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=5720445
rawauthor: Jianxun Chen and Yongzhong Huang and Shaozhong Guo and Shimiao Chen and Wei Wang
rawbooktitle: {2011 Third International Conference on Measuring Technology and Mechatronics Automation (ICMTMA)}
rawtitle: Test Standardization and Analyse Model of Mathematical Functions for Precision
abstract:
This article describes problems of meet the requirements to implementations of mathematical functions working with floating-point numbers, and so facilitate the comprehensive testing of mathematical functions. Inconsistency and incompleteness of available standards in the domain is demonstrated. Correct rounding requirement is suggested to guarantee preservation of all important properties of functions and to support high level of interoperability between different mathematical libraries and software using them. The article also concerns precision analyse of mathematical functions. Conformance test construction method is proposed based on different sources of test data.

remark:
This paper contains unattributed plagiaristic copying of material from url https://www.math.utah.edu/~beebe/software/ieee/index.html.

rawabstract:
This article describes problems of meet the requirements to implementations of mathematical functions working with floating-point numbers, and so facilitate the comprehensive testing of mathematical functions. Inconsistency and incompleteness of available standards in the domain is demonstrated. Correct rounding requirement is suggested to guarantee preservation of all important properties of functions and to support high level of interoperability between different mathematical libraries and software using them. The article also concerns precision analyse of mathematical functions. Conformance test construction method is proposed based on different sources of test data.

entry:
@InProceedings{Chen:2011:TSA,
  author =       "Jianxun Chen and Yongzhong Huang and Shaozhong Guo and
                 Shimiao Chen and Wei Wang",
  booktitle =    "{2011 Third International Conference on Measuring
                 Technology and Mechatronics Automation (ICMTMA)}",
  title =        "Test Standardization and Analyse Model of Mathematical
                 Functions for Precision",
  volume =       "3",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "652--655",
  year =         "2011",
  DOI =          "https://doi.org/10.1109/ICMTMA.2011.734",
  ISBN =         "0-7695-4296-4",
  ISBN-13 =      "978-0-7695-4296-6",
  bibdate =      "Tue Sep 27 08:11:02 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5721571",
  abstract =     "This article describes problems of meet the
                 requirements to implementations of mathematical
                 functions working with floating-point numbers, and so
                 facilitate the comprehensive testing of mathematical
                 functions. Inconsistency and incompleteness of
                 available standards in the domain is demonstrated.
                 Correct rounding requirement is suggested to guarantee
                 preservation of all important properties of functions
                 and to support high level of interoperability between
                 different mathematical libraries and software using
                 them. The article also concerns precision analyse of
                 mathematical functions. Conformance test construction
                 method is proposed based on different sources of test
                 data.",
  acknowledgement = ack-nhfb,
  book-URL =     "http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=5720445",
  remark =       "This paper contains unattributed plagiaristic copying
                 of material from
                 \url{https://www.math.utah.edu/~beebe/software/ieee/index.html}.",
}


bibtype: article
filename: elefunt.bib
label: Chlebus:2011:RSI
author: Edward Chlebus
title: A Recursive Scheme for Improving the Original Rate of Convergence to the Euler--Mascheroni Constant
journal: j-AMER-MATH-MONTHLY
volume: 118
number: 3
pages: 268--274
month: mar
monthnumber: 3
year: 2011
CODEN: AMMYAE
DOI: https://doi.org/10.4169/amer.math.monthly.118.03.268
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
bibdate: Mon Jan 30 08:58:19 MST 2012
bibtimestamp: 2012.01.30 08:58:19 MST
URL: http://www.jstor.org/stable/pdfplus/10.4169/amer.math.monthly.118.03.268.pdf
fjournal: American Mathematical Monthly
acknowledgement: ack-nhfb
journalURL: https://www.jstor.org/journals/00029890.htm
rawauthor: Edward Chlebus
bibsource:
http://www.jstor.org/journals/00029890.html; http://www.jstor.org/stable/10.4169/amermathmont.118.issue-3; https://www.math.utah.edu/pub/tex/bib/amermathmonthly2010.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

abstract:
We have used Euler--Maclaurin summation to develop a recursive scheme for modifying the original approximation for the Euler--Mascheroni constant $ gamma $. Convergence to $ gamma $ resulting from successively employing the proposed scheme has been significantly accelerated while the form of the approximation originally introduced by Euler is still preserved.

remark:
The author derives relations between $ gamma $ and the $n$-th partial sum of the harmonic series that have an error $ O(n^-2 k) $ for increasing $k$. He also references prior work from 2009 that computes $ gamma $ to 29,844,489,545 decimal digits.

rawabstract:
We have used Euler--Maclaurin summation to develop a recursive scheme for modifying the original approximation for the Euler--Mascheroni constant $ \gamma $. Convergence to $ \gamma $ resulting from successively employing the proposed scheme has been significantly accelerated while the form of the approximation originally introduced by Euler is still preserved.

rawtitle:
A Recursive Scheme for Improving the Original Rate of Convergence to the {Euler--Mascheroni} Constant

entry:
@Article{Chlebus:2011:RSI,
  author =       "Edward Chlebus",
  title =        "A Recursive Scheme for Improving the Original Rate of
                 Convergence to the {Euler--Mascheroni} Constant",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "118",
  number =       "3",
  pages =        "268--274",
  month =        mar,
  year =         "2011",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.4169/amer.math.monthly.118.03.268",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Mon Jan 30 08:58:19 MST 2012",
  bibsource =    "http://www.jstor.org/journals/00029890.html;
                 http://www.jstor.org/stable/10.4169/amermathmont.118.issue-3;
                 https://www.math.utah.edu/pub/tex/bib/amermathmonthly2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.jstor.org/stable/pdfplus/10.4169/amer.math.monthly.118.03.268.pdf",
  abstract =     "We have used Euler--Maclaurin summation to develop a
                 recursive scheme for modifying the original
                 approximation for the Euler--Mascheroni constant $
                 \gamma $. Convergence to $ \gamma $ resulting from
                 successively employing the proposed scheme has been
                 significantly accelerated while the form of the
                 approximation originally introduced by Euler is still
                 preserved.",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
  remark =       "The author derives relations between $ \gamma $ and
                 the $n$-th partial sum of the harmonic series that have
                 an error $ O(n^{-2 k}) $ for increasing $k$. He also
                 references prior work from 2009 that computes $ \gamma
                 $ to 29,844,489,545 decimal digits.",
}


bibtype: article
filename: elefunt.bib
label: Choi:2011:AFT
author: Junesang Choi and H. M. Srivastava
journal: j-APPL-MATH-COMP
volume: 218
number: 6
pages: 2631--2640
day: 15
month: nov
monthnumber: 11
year: 2011
CODEN: AMHCBQ
DOI: https://doi.org/10.1016/j.amc.2011.08.002
ISSN: 0096-3003 (print), 1873-5649 (electronic) OR 00963003 (print), 18735649 (electronic)
ISSNL: 0096-3003 OR 00963003
bibdate: Tue Oct 25 09:03:08 MDT 2011
bibtimestamp: 2011.10.25 09:03:08 MDT
URL: http://www.sciencedirect.com/science/article/pii/S0096300311010289
fjournal: Applied Mathematics and Computation
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00963003
rawauthor: Junesang Choi and H. M. Srivastava
title:
Asymptotic formulas for the triple Gamma function $ Gamma _3 $ by means of its integral representation

bibsource:
http://www.sciencedirect.com/science/journal/00963003; https://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

rawtitle:
Asymptotic formulas for the triple {Gamma} function {$ \Gamma_3 $} by means of its integral representation

entry:
@Article{Choi:2011:AFT,
  author =       "Junesang Choi and H. M. Srivastava",
  title =        "Asymptotic formulas for the triple {Gamma} function {$
                 \Gamma_3 $} by means of its integral representation",
  journal =      j-APPL-MATH-COMP,
  volume =       "218",
  number =       "6",
  pages =        "2631--2640",
  day =          "15",
  month =        nov,
  year =         "2011",
  CODEN =        "AMHCBQ",
  DOI =          "https://doi.org/10.1016/j.amc.2011.08.002",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Tue Oct 25 09:03:08 MDT 2011",
  bibsource =    "http://www.sciencedirect.com/science/journal/00963003;
                 https://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0096300311010289",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
}


bibtype: article
filename: elefunt.bib
label: Colman:2011:VCC
author: Michel Colman and Annie Cuyt and Joris Van Deun
title: Validated computation of certain hypergeometric functions
journal: j-TOMS
volume: 38
number: 2
pages: 11:1--11:20
month: dec
monthnumber: 12
year: 2011
CODEN: ACMSCU
DOI: https://doi.org/10.1145/2049673.2049675
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Fri Dec 30 17:43:07 MST 2011
bibtimestamp: 2011.12.30 17:43:07 MST
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
articleno: 11
journalURL: https://dl.acm.org/loi/toms
rawauthor: Michel Colman and Annie Cuyt and Joris {Van Deun}
rawtitle: Validated computation of certain hypergeometric functions
abstract:
We present an efficient algorithm for the validated high-precision computation of real continued fractions, accurate to the last digit. The algorithm proceeds in two stages. In the first stage, computations are done in double precision. A forward error analysis and some heuristics are used to obtain an a priori error estimate. This estimate is used in the second stage to compute the fraction to the requested accuracy in high precision (adaptively incrementing the precision for reasons of efficiency). A running error analysis and techniques from interval arithmetic are used to validate the result.

rawabstract:
We present an efficient algorithm for the validated high-precision computation of real continued fractions, accurate to the last digit. The algorithm proceeds in two stages. In the first stage, computations are done in double precision. A forward error analysis and some heuristics are used to obtain an a priori error estimate. This estimate is used in the second stage to compute the fraction to the requested accuracy in high precision (adaptively incrementing the precision for reasons of efficiency). A running error analysis and techniques from interval arithmetic are used to validate the result.

entry:
@Article{Colman:2011:VCC,
  author =       "Michel Colman and Annie Cuyt and Joris {Van Deun}",
  title =        "Validated computation of certain hypergeometric
                 functions",
  journal =      j-TOMS,
  volume =       "38",
  number =       "2",
  pages =        "11:1--11:20",
  month =        dec,
  year =         "2011",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2049673.2049675",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Dec 30 17:43:07 MST 2011",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We present an efficient algorithm for the validated
                 high-precision computation of real continued fractions,
                 accurate to the last digit. The algorithm proceeds in
                 two stages. In the first stage, computations are done
                 in double precision. A forward error analysis and some
                 heuristics are used to obtain an a priori error
                 estimate. This estimate is used in the second stage to
                 compute the fraction to the requested accuracy in high
                 precision (adaptively incrementing the precision for
                 reasons of efficiency). A running error analysis and
                 techniques from interval arithmetic are used to
                 validate the result.",
  acknowledgement = ack-nhfb,
  articleno =    "11",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: article
filename: elefunt.bib
label: deDinechin:2011:CFP
author: Florent de Dinechin and Christoph Lauter and Guillaume Melquiond
title: Certifying the Floating-Point Implementation of an Elementary Function Using Gappa
journal: j-IEEE-TRANS-COMPUT
volume: 60
number: 2
pages: 242--253
month: feb
monthnumber: 2
year: 2011
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.2010.128
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sun Feb 20 19:15:33 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2011.02.20 19:15:33 ???
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Florent de Dinechin and Christoph Lauter and Guillaume Melquiond
rawtitle: Certifying the Floating-Point Implementation of an Elementary Function Using {Gappa}
abstract:
High confidence in floating-point programs requires proving numerical properties of final and intermediate values. One may need to guarantee that a value stays within some range, or that the error relative to some ideal value is well bounded. This certification may require a time-consuming proof for each line of code, and it is usually broken by the smallest change to the code, e.g., for maintenance or optimization purpose. Certifying floating-point programs by hand is, therefore, very tedious and error-prone. The Gappa proof assistant is designed to make this task both easier and more secure, due to the following novel features: It automates the evaluation and propagation of rounding errors using interval arithmetic. Its input format is very close to the actual code to validate. It can be used incrementally to prove complex mathematical properties pertaining to the code. It generates a formal proof of the results, which can be checked independently by a lower level proof assistant like Coq. Yet it does not require any specific knowledge about automatic theorem proving, and thus, is accessible to a wide community. This paper demonstrates the practical use of this tool for a widely used class of floating-point programs: implementations of elementary functions in a mathematical library.

rawabstract:
High confidence in floating-point programs requires proving numerical properties of final and intermediate values. One may need to guarantee that a value stays within some range, or that the error relative to some ideal value is well bounded. This certification may require a time-consuming proof for each line of code, and it is usually broken by the smallest change to the code, e.g., for maintenance or optimization purpose. Certifying floating-point programs by hand is, therefore, very tedious and error-prone. The Gappa proof assistant is designed to make this task both easier and more secure, due to the following novel features: It automates the evaluation and propagation of rounding errors using interval arithmetic. Its input format is very close to the actual code to validate. It can be used incrementally to prove complex mathematical properties pertaining to the code. It generates a formal proof of the results, which can be checked independently by a lower level proof assistant like Coq. Yet it does not require any specific knowledge about automatic theorem proving, and thus, is accessible to a wide community. This paper demonstrates the practical use of this tool for a widely used class of floating-point programs: implementations of elementary functions in a mathematical library.

entry:
@Article{deDinechin:2011:CFP,
  author =       "Florent de Dinechin and Christoph Lauter and Guillaume
                 Melquiond",
  title =        "Certifying the Floating-Point Implementation of an
                 Elementary Function Using {Gappa}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "60",
  number =       "2",
  pages =        "242--253",
  month =        feb,
  year =         "2011",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2010.128",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Feb 20 19:15:33 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "High confidence in floating-point programs requires
                 proving numerical properties of final and intermediate
                 values. One may need to guarantee that a value stays
                 within some range, or that the error relative to some
                 ideal value is well bounded. This certification may
                 require a time-consuming proof for each line of code,
                 and it is usually broken by the smallest change to the
                 code, e.g., for maintenance or optimization purpose.
                 Certifying floating-point programs by hand is,
                 therefore, very tedious and error-prone. The Gappa
                 proof assistant is designed to make this task both
                 easier and more secure, due to the following novel
                 features: It automates the evaluation and propagation
                 of rounding errors using interval arithmetic. Its input
                 format is very close to the actual code to validate. It
                 can be used incrementally to prove complex mathematical
                 properties pertaining to the code. It generates a
                 formal proof of the results, which can be checked
                 independently by a lower level proof assistant like
                 Coq. Yet it does not require any specific knowledge
                 about automatic theorem proving, and thus, is
                 accessible to a wide community. This paper demonstrates
                 the practical use of this tool for a widely used class
                 of floating-point programs: implementations of
                 elementary functions in a mathematical library.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: elefunt.bib
label: Fu:2011:ETB
author: Hua Fu and Pooi-Yuen Kam
booktitle: 2011 IEEE Global Telecommunications Conference --- GLOBECOM 2011
title: Exponential-Type Bounds on the First-Order Marcum Q-Function
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 242--253
month: dec
monthnumber: 12
year: 2011
DOI: https://doi.org/10.1109/glocom.2011.6133801
bibdate: Sat Dec 16 16:28:28 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.12.16 16:28:28 ???
URL: http://ieeexplore.ieee.org/document/6133801/
acknowledgement: ack-nhfb
rawauthor: Hua Fu and Pooi-Yuen Kam
rawbooktitle: 2011 {IEEE} Global Telecommunications Conference --- {GLOBECOM 2011}
rawtitle: Exponential-Type Bounds on the First-Order {Marcum} Q-Function
entry:
@InProceedings{Fu:2011:ETB,
  author =       "Hua Fu and Pooi-Yuen Kam",
  booktitle =    "2011 {IEEE} Global Telecommunications Conference ---
                 {GLOBECOM 2011}",
  title =        "Exponential-Type Bounds on the First-Order {Marcum}
                 Q-Function",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  month =        dec,
  year =         "2011",
  DOI =          "https://doi.org/10.1109/glocom.2011.6133801",
  bibdate =      "Sat Dec 16 16:28:28 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://ieeexplore.ieee.org/document/6133801/",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Fukushima:2011:PFC
author: Toshio Fukushima
title: Precise and fast computation of the general complete elliptic integral of the second kind
journal: j-MATH-COMPUT
volume: 80
number: 275
pages: 1725--1743
month: jul
monthnumber: 7
year: 2011
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Mon Apr 18 06:32:30 MDT 2011
bibsource: http://www.ams.org/mcom/2011-80-275; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2011.04.18 06:32:30 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Toshio Fukushima
rawtitle: Precise and fast computation of the general complete elliptic integral of the second kind
URL:
http://www.ams.org/journals/mcom/2011-80-275/S0025-5718-2011-02455-5/home.html; http://www.ams.org/journals/mcom/2011-80-275/S0025-5718-2011-02455-5/S0025-5718-2011-02455-5.pdf

abstract:
We developed an efficient procedure to evaluate two auxiliary complete elliptic integrals of the second kind $ B(m) $ and $ D(m) $ by using their Taylor series expansions, the definition of Jacobi's nome, and Legendre's relation. The developed procedure is more precise than the existing ones in the sense that the maximum relative errors are 1--3 machine epsilons, and it runs drastically faster; around 5 times faster than Bulirsch's cel2 and 16 times faster than Carlson's $ R_F $ and $ R_D $.

rawabstract:
We developed an efficient procedure to evaluate two auxiliary complete elliptic integrals of the second kind $ B(m) $ and $ D(m) $ by using their Taylor series expansions, the definition of Jacobi's nome, and Legendre's relation. The developed procedure is more precise than the existing ones in the sense that the maximum relative errors are 1--3 machine epsilons, and it runs drastically faster; around 5 times faster than Bulirsch's cel2 and 16 times faster than Carlson's $ R_F $ and $ R_D $.

entry:
@Article{Fukushima:2011:PFC,
  author =       "Toshio Fukushima",
  title =        "Precise and fast computation of the general complete
                 elliptic integral of the second kind",
  journal =      j-MATH-COMPUT,
  volume =       "80",
  number =       "275",
  pages =        "1725--1743",
  month =        jul,
  year =         "2011",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Mon Apr 18 06:32:30 MDT 2011",
  bibsource =    "http://www.ams.org/mcom/2011-80-275;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.ams.org/journals/mcom/2011-80-275/S0025-5718-2011-02455-5/home.html;
                 http://www.ams.org/journals/mcom/2011-80-275/S0025-5718-2011-02455-5/S0025-5718-2011-02455-5.pdf",
  abstract =     "We developed an efficient procedure to evaluate two
                 auxiliary complete elliptic integrals of the second
                 kind $ B(m) $ and $ D(m) $ by using their Taylor series
                 expansions, the definition of Jacobi's nome, and
                 Legendre's relation. The developed procedure is more
                 precise than the existing ones in the sense that the
                 maximum relative errors are 1--3 machine epsilons, and
                 it runs drastically faster; around 5 times faster than
                 Bulirsch's cel2 and 16 times faster than Carlson's $
                 R_F $ and $ R_D $.",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Gautschi:2011:LWF
author: Walter Gautschi
title: The Lambert $W$-functions and some of their integrals: a case study of high-precision computation
journal: j-NUMER-ALGORITHMS
volume: 57
number: 1
pages: 27--34
month: may
monthnumber: 5
year: 2011
CODEN: NUALEG
DOI: https://doi.org/10.1007/s11075-010-9409-6
ISSN: 1017-1398 (print), 1572-9265 (electronic) OR 10171398 (print), 15729265 (electronic)
ISSNL: 1017-1398 OR 10171398
bibdate: Wed Apr 27 08:44:14 MDT 2011
bibtimestamp: 2011.04.27 08:44:14 MDT
URL: http://www.springerlink.com/openurl.asp?genre=article&issn=1017-1398&volume=57&issue=1&spage=27
fjournal: Numerical Algorithms
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/11075
rawauthor: Walter Gautschi
bibsource:
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1017-1398&volume=57&issue=1; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

abstract:
The real-valued Lambert W-functions considered here are $ w_0 (y) $ and $ w_-1(y) $, solutions of $ w e^w = y $, $ - 1 / e < y < 0 $, with values respectively in $ ( - 1, 0) $ and $ ( - infty , - 1) $. A study is made of the numerical evaluation to high precision of these functions and of the integrals, $ alpha > 0 $, $ beta in mathbb R $, and $ alpha > - 1 $, $ beta < 1 $. For the latter we use known integral representations and their evaluation by nonstandard Gaussian quadrature, if $ alpha neq beta $, and explicit formulae involving the trigamma function, if $ alpha = beta $.

keywords:
Integrals of Lambert W-functions; Lambert W-functions; Nonstandard Gaussian quadrature; Variable-precision computation

rawabstract:
The real-valued Lambert W-functions considered here are $ w_0 (y) $ and $ w_{-1}(y) $, solutions of $ w e^w = y $, $ - 1 / e < y < 0 $, with values respectively in $ ( - 1, 0) $ and $ ( - \infty, - 1) $. A study is made of the numerical evaluation to high precision of these functions and of the integrals, $ \alpha > 0 $, $ \beta \in \mathbb {R} $, and $ \alpha > - 1 $, $ \beta < 1 $. For the latter we use known integral representations and their evaluation by nonstandard Gaussian quadrature, if $ \alpha \neq \beta $, and explicit formulae involving the trigamma function, if $ \alpha = \beta $.

rawtitle:
The {Lambert} {$W$}-functions and some of their integrals: a case study of high-precision computation

entry:
@Article{Gautschi:2011:LWF,
  author =       "Walter Gautschi",
  title =        "The {Lambert} {$W$}-functions and some of their
                 integrals: a case study of high-precision computation",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "57",
  number =       "1",
  pages =        "27--34",
  month =        may,
  year =         "2011",
  CODEN =        "NUALEG",
  DOI =          "https://doi.org/10.1007/s11075-010-9409-6",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Wed Apr 27 08:44:14 MDT 2011",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1017-1398&volume=57&issue=1;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=1017-1398&volume=57&issue=1&spage=27",
  abstract =     "The real-valued Lambert W-functions considered here
                 are $ w_0 (y) $ and $ w_{-1}(y) $, solutions of $ w e^w
                 = y $, $ - 1 / e < y < 0 $, with values respectively in
                 $ ( - 1, 0) $ and $ ( - \infty, - 1) $. A study is made
                 of the numerical evaluation to high precision of these
                 functions and of the integrals, $ \alpha > 0 $, $ \beta
                 \in \mathbb {R} $, and $ \alpha > - 1 $, $ \beta < 1 $.
                 For the latter we use known integral representations
                 and their evaluation by nonstandard Gaussian
                 quadrature, if $ \alpha \neq \beta $, and explicit
                 formulae involving the trigamma function, if $ \alpha =
                 \beta $.",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
  keywords =     "Integrals of Lambert W-functions; Lambert W-functions;
                 Nonstandard Gaussian quadrature; Variable-precision
                 computation",
}


bibtype: article
filename: elefunt.bib
label: Gil:2011:APC
author: Amparo Gil and Javier Segura and Nico M. Temme
title: Algorithm 914: Parabolic cylinder function $ W(a, x) $ and its derivative
journal: j-TOMS
volume: 38
number: 1
pages: 6:1--6:5
month: nov
monthnumber: 11
year: 2011
CODEN: ACMSCU
DOI: https://doi.org/10.1145/2049662.2049668
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Thu Dec 15 08:59:34 MST 2011
bibtimestamp: 2011.12.15 08:59:34 MST
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
articleno: 6
journalURL: https://dl.acm.org/loi/toms
rawauthor: Amparo Gil and Javier Segura and Nico M. Temme
rawtitle: {Algorithm 914}: {Parabolic} cylinder function {$ W(a, x) $} and its derivative
bibsource:
http://www.acm.org/pubs/contents/journals/toms/; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fortran3.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib

abstract:
A Fortran 90 program for the computation of the real parabolic cylinder functions $ W(a, pm x) $, $ x geq 0 $ and their derivatives is presented. The code also computes scaled functions for $ a > 50 $. The functions $ W(a, pm x) $ are a numerically satisfactory pair of solutions of the parabolic cylinder equation $ y^prime + (x^2 / 4 - a)y = 0 $, $ x geq 0 $. Using Wronskian tests, we claim a relative accuracy better than $ 5 times 10^-13 $ in the computable range of unscaled functions, while for scaled functions the aimed relative accuracy is better than $ 5 times 10^-14 $. This code, together with the algorithm and related software described in Gil et al.

rawabstract:
A Fortran 90 program for the computation of the real parabolic cylinder functions $ W(a, \pm x) $, $ x \geq 0 $ and their derivatives is presented. The code also computes scaled functions for $ a > 50 $. The functions $ W(a, \pm x) $ are a numerically satisfactory pair of solutions of the parabolic cylinder equation $ y^\prime + (x^2 / 4 - a)y = 0 $, $ x \geq 0 $. Using Wronskian tests, we claim a relative accuracy better than $ 5 \times 10^{-13} $ in the computable range of unscaled functions, while for scaled functions the aimed relative accuracy is better than $ 5 \times 10^{-14} $. This code, together with the algorithm and related software described in Gil et al.

entry:
@Article{Gil:2011:APC,
  author =       "Amparo Gil and Javier Segura and Nico M. Temme",
  title =        "{Algorithm 914}: {Parabolic} cylinder function {$ W(a,
                 x) $} and its derivative",
  journal =      j-TOMS,
  volume =       "38",
  number =       "1",
  pages =        "6:1--6:5",
  month =        nov,
  year =         "2011",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2049662.2049668",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Dec 15 08:59:34 MST 2011",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "A Fortran 90 program for the computation of the real
                 parabolic cylinder functions $ W(a, \pm x) $, $ x \geq
                 0 $ and their derivatives is presented. The code also
                 computes scaled functions for $ a > 50 $. The functions
                 $ W(a, \pm x) $ are a numerically satisfactory pair of
                 solutions of the parabolic cylinder equation $ y^\prime
                 + (x^2 / 4 - a)y = 0 $, $ x \geq 0 $. Using Wronskian
                 tests, we claim a relative accuracy better than $ 5
                 \times 10^{-13} $ in the computable range of unscaled
                 functions, while for scaled functions the aimed
                 relative accuracy is better than $ 5 \times 10^{-14} $.
                 This code, together with the algorithm and related
                 software described in Gil et al.",
  acknowledgement = ack-nhfb,
  articleno =    "6",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: article
filename: elefunt.bib
label: Gil:2011:FAC
author: Amparo Gil and Javier Segura and Nico M. Temme
title: Fast and accurate computation of the Weber parabolic cylinder function $ W(a, x) $
journal: j-IMA-J-NUMER-ANAL
volume: 31
number: 3
pages: 1194--1216
month: jul
monthnumber: 7
year: 2011
CODEN: IJNADH
DOI: https://doi.org/10.1093/imanum/drq012
ISSN: 0272-4979 (print), 1464-3642 (electronic) OR 02724979 (print), 14643642 (electronic)
ISSNL: 0272-4979 OR 02724979
bibdate: Fri Jul 15 12:37:42 MDT 2011
bibtimestamp: 2011.07.15 12:37:42 MDT
URL: http://imajna.oxfordjournals.org/content/31/3/1194.full.pdf+html
fjournal: IMA Journal of Numerical Analysis
acknowledgement: ack-nhfb
journalURL: http://imajna.oxfordjournals.org/content/by/year
onlinedate: July 7, 2010
rawauthor: Amparo Gil and Javier Segura and Nico M. Temme
rawtitle: Fast and accurate computation of the {Weber} parabolic cylinder function {$ W(a, x) $}
bibsource:
http://imanum.oxfordjournals.org/content/31/3.toc; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Gil:2011:FAC,
  author =       "Amparo Gil and Javier Segura and Nico M. Temme",
  title =        "Fast and accurate computation of the {Weber} parabolic
                 cylinder function {$ W(a, x) $}",
  journal =      j-IMA-J-NUMER-ANAL,
  volume =       "31",
  number =       "3",
  pages =        "1194--1216",
  month =        jul,
  year =         "2011",
  CODEN =        "IJNADH",
  DOI =          "https://doi.org/10.1093/imanum/drq012",
  ISSN =         "0272-4979 (print), 1464-3642 (electronic)",
  ISSN-L =       "0272-4979",
  bibdate =      "Fri Jul 15 12:37:42 MDT 2011",
  bibsource =    "http://imanum.oxfordjournals.org/content/31/3.toc;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://imajna.oxfordjournals.org/content/31/3/1194.full.pdf+html",
  acknowledgement = ack-nhfb,
  fjournal =     "IMA Journal of Numerical Analysis",
  journal-URL =  "http://imajna.oxfordjournals.org/content/by/year",
  onlinedate =   "July 7, 2010",
}


bibtype: article
filename: elefunt.bib
label: Jaime:2011:HSA
author: F. J. Jaime and M. A. Sanchez and J. Hormigo and J. Villalba and E. L. Zapata
title: High-Speed Algorithms and Architectures for Range Reduction Computation
journal: j-IEEE-TRANS-VLSI-SYST
volume: 19
number: 3
pages: 512--516
year: 2011
CODEN: IEVSE9
DOI: https://doi.org/10.1109/TVLSI.2009.2033932
ISSN: 1063-8210 (print), 1557-9999 (electronic) OR 10638210 (print), 15579999 (electronic)
ISSNL: 1063-8210 OR 10638210
bibdate: Tue Sep 27 08:11:02 MDT 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2011.09.27 08:11:02 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5308221
fjournal: IEEE Transactions on Very Large Scale Integration (VLSI) Systems
acknowledgement: ack-nhfb
bookURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=92
rawauthor: F. J. Jaime and M. A. S{\'a}nchez and J. Hormigo and J. Villalba and E. L. Zapata
rawtitle: High-Speed Algorithms and Architectures for Range Reduction Computation
abstract:
Range reduction is a crucial step for accuracy in trigonometric functions evaluation. This paper shows and compares a set of algorithms for additive range reduction computation and their corresponding application-specific integrated circuit implementations (ensuring an accuracy of one unit in the last place). A word-serial architecture implementation has been used as a reference for clearer comparisons. Besides, a new table-based pipelined architecture for range reduction has also been proposed.

rawabstract:
Range reduction is a crucial step for accuracy in trigonometric functions evaluation. This paper shows and compares a set of algorithms for additive range reduction computation and their corresponding application-specific integrated circuit implementations (ensuring an accuracy of one unit in the last place). A word-serial architecture implementation has been used as a reference for clearer comparisons. Besides, a new table-based pipelined architecture for range reduction has also been proposed.

entry:
@Article{Jaime:2011:HSA,
  author =       "F. J. Jaime and M. A. S{\'a}nchez and J. Hormigo and
                 J. Villalba and E. L. Zapata",
  title =        "High-Speed Algorithms and Architectures for Range
                 Reduction Computation",
  journal =      j-IEEE-TRANS-VLSI-SYST,
  volume =       "19",
  number =       "3",
  pages =        "512--516",
  month =        "????",
  year =         "2011",
  CODEN =        "IEVSE9",
  DOI =          "https://doi.org/10.1109/TVLSI.2009.2033932",
  ISSN =         "1063-8210 (print), 1557-9999 (electronic)",
  ISSN-L =       "1063-8210",
  bibdate =      "Tue Sep 27 08:11:02 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5308221",
  abstract =     "Range reduction is a crucial step for accuracy in
                 trigonometric functions evaluation. This paper shows
                 and compares a set of algorithms for additive range
                 reduction computation and their corresponding
                 application-specific integrated circuit implementations
                 (ensuring an accuracy of one unit in the last place). A
                 word-serial architecture implementation has been used
                 as a reference for clearer comparisons. Besides, a new
                 table-based pipelined architecture for range reduction
                 has also been proposed.",
  acknowledgement = ack-nhfb,
  book-URL =     "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=92",
  fjournal =     "IEEE Transactions on Very Large Scale Integration
                 (VLSI) Systems",
}


bibtype: article
filename: elefunt.bib
label: Jang:2011:CTS
author: Won Mee Jang
title: Corrections to ``A Simple Upper Bound of the Gaussian $Q$-Function with Closed-form Error Bound''
journal: j-IEEE-COMMUN-LET
volume: 15
number: 12
pages: 1274--1274
month: dec
monthnumber: 12
year: 2011
CODEN: ICLEF6
DOI: https://doi.org/10.1109/lcomm.2011.101911.111996
ISSN: 1089-7798 (print), 1558-2558 (electronic) OR 10897798 (print), 15582558 (electronic)
ISSNL: 1089-7798 OR 10897798
bibdate: Sat Dec 16 16:46:05 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.12.16 16:46:05 ???
URL: http://ieeexplore.ieee.org/document/6065242/
fjournal: IEEE Communications Letters
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4234
rawauthor: Won Mee Jang
rawtitle: Corrections to {``A Simple Upper Bound of the Gaussian $Q$-Function with Closed-form Error Bound''}
entry:
@Article{Jang:2011:CTS,
  author =       "Won Mee Jang",
  title =        "Corrections to {``A Simple Upper Bound of the Gaussian
                 $Q$-Function with Closed-form Error Bound''}",
  journal =      j-IEEE-COMMUN-LET,
  volume =       "15",
  number =       "12",
  pages =        "1274--1274",
  month =        dec,
  year =         "2011",
  CODEN =        "ICLEF6",
  DOI =          "https://doi.org/10.1109/lcomm.2011.101911.111996",
  ISSN =         "1089-7798 (print), 1558-2558 (electronic)",
  ISSN-L =       "1089-7798",
  bibdate =      "Sat Dec 16 16:46:05 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://ieeexplore.ieee.org/document/6065242/",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Communications Letters",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4234",
}


bibtype: article
filename: elefunt.bib
label: Jang:2011:SUB
author: Won Mee Jang
title: A Simple Upper Bound of the Gaussian $Q$-Function with Closed-Form Error Bound
journal: j-IEEE-COMMUN-LET
volume: 15
number: 2
pages: 157--159
month: feb
monthnumber: 2
year: 2011
CODEN: ICLEF6
DOI: https://doi.org/10.1109/lcomm.2011.011011.102207
ISSN: 1089-7798 (print), 1558-2558 (electronic) OR 10897798 (print), 15582558 (electronic)
ISSNL: 1089-7798 OR 10897798
bibdate: Sat Dec 16 16:47:28 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.12.16 16:47:28 ???
URL: http://ieeexplore.ieee.org/document/5692888/
fjournal: IEEE Communications Letters
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4234
rawauthor: Won Mee Jang
rawtitle: A Simple Upper Bound of the {Gaussian} {$Q$}-Function with Closed-Form Error Bound
entry:
@Article{Jang:2011:SUB,
  author =       "Won Mee Jang",
  title =        "A Simple Upper Bound of the {Gaussian} {$Q$}-Function
                 with Closed-Form Error Bound",
  journal =      j-IEEE-COMMUN-LET,
  volume =       "15",
  number =       "2",
  pages =        "157--159",
  month =        feb,
  year =         "2011",
  CODEN =        "ICLEF6",
  DOI =          "https://doi.org/10.1109/lcomm.2011.011011.102207",
  ISSN =         "1089-7798 (print), 1558-2558 (electronic)",
  ISSN-L =       "1089-7798",
  bibdate =      "Sat Dec 16 16:47:28 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://ieeexplore.ieee.org/document/5692888/",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Communications Letters",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4234",
}


bibtype: article
filename: elefunt.bib
label: Jeannerod:2011:CFP
author: Claude-Pierre Jeannerod and Herve Knochel and Christophe Monat and Guillaume Revy
title: Computing Floating-Point Square Roots via Bivariate Polynomial Evaluation
journal: j-IEEE-TRANS-COMPUT
volume: 60
number: 2
pages: 214--227
month: feb
monthnumber: 2
year: 2011
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.2010.152
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sun Feb 20 19:15:33 2011
bibtimestamp: 2011.02.20 19:15:33 ???
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Claude-Pierre Jeannerod and Herv{\'e} Knochel and Christophe Monat and Guillaume Revy
rawtitle: Computing Floating-Point Square Roots via Bivariate Polynomial Evaluation
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib

abstract:
In this paper, we show how to reduce the computation of correctly rounded square roots of binary floating-point data to the fixed-point evaluation of some particular integer polynomials in two variables. By designing parallel and accurate evaluation schemes for such bivariate polynomials, we show further that this approach allows for high instruction-level parallelism (ILP) exposure, and thus, potentially low-latency implementations. Then, as an illustration, we detail a C implementation of our method in the case of IEEE 754-2008 binary32 floating-point data (formerly called single precision in the 1985 version of the IEEE 754 standard). This software implementation, which assumes 32-bit unsigned integer arithmetic only, is almost complete in the sense that it supports special operands, subnormal numbers, and all rounding-direction attributes, but not exception handling (that is, status flags are not set). Finally, we have carried out experiments with this implementation on the ST231, an integer processor from the STMicroelectronics' ST200 family, using the ST200 family VLIW compiler. The results obtained demonstrate the practical interest of our approach in that context: for all rounding-direction attributes, the generated assembly code is optimally scheduled and has indeed low latency (23 cycles).

rawabstract:
In this paper, we show how to reduce the computation of correctly rounded square roots of binary floating-point data to the fixed-point evaluation of some particular integer polynomials in two variables. By designing parallel and accurate evaluation schemes for such bivariate polynomials, we show further that this approach allows for high instruction-level parallelism (ILP) exposure, and thus, potentially low-latency implementations. Then, as an illustration, we detail a C implementation of our method in the case of IEEE 754-2008 binary32 floating-point data (formerly called single precision in the 1985 version of the IEEE 754 standard). This software implementation, which assumes 32-bit unsigned integer arithmetic only, is almost complete in the sense that it supports special operands, subnormal numbers, and all rounding-direction attributes, but not exception handling (that is, status flags are not set). Finally, we have carried out experiments with this implementation on the ST231, an integer processor from the STMicroelectronics' ST200 family, using the ST200 family VLIW compiler. The results obtained demonstrate the practical interest of our approach in that context: for all rounding-direction attributes, the generated assembly code is optimally scheduled and has indeed low latency (23 cycles).

entry:
@Article{Jeannerod:2011:CFP,
  author =       "Claude-Pierre Jeannerod and Herv{\'e} Knochel and
                 Christophe Monat and Guillaume Revy",
  title =        "Computing Floating-Point Square Roots via Bivariate
                 Polynomial Evaluation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "60",
  number =       "2",
  pages =        "214--227",
  month =        feb,
  year =         "2011",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2010.152",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Feb 20 19:15:33 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  abstract =     "In this paper, we show how to reduce the computation
                 of correctly rounded square roots of binary
                 floating-point data to the fixed-point evaluation of
                 some particular integer polynomials in two variables.
                 By designing parallel and accurate evaluation schemes
                 for such bivariate polynomials, we show further that
                 this approach allows for high instruction-level
                 parallelism (ILP) exposure, and thus, potentially
                 low-latency implementations. Then, as an illustration,
                 we detail a C implementation of our method in the case
                 of IEEE 754-2008 binary32 floating-point data (formerly
                 called single precision in the 1985 version of the IEEE
                 754 standard). This software implementation, which
                 assumes 32-bit unsigned integer arithmetic only, is
                 almost complete in the sense that it supports special
                 operands, subnormal numbers, and all rounding-direction
                 attributes, but not exception handling (that is, status
                 flags are not set). Finally, we have carried out
                 experiments with this implementation on the ST231, an
                 integer processor from the STMicroelectronics' ST200
                 family, using the ST200 family VLIW compiler. The
                 results obtained demonstrate the practical interest of
                 our approach in that context: for all
                 rounding-direction attributes, the generated assembly
                 code is optimally scheduled and has indeed low latency
                 (23 cycles).",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: elefunt.bib
label: Johansson:2011:CRE
author: Bo Goran Johansson
title: Cube root extraction in medieval mathematics
journal: j-HIST-MATH
volume: 38
number: 3
pages: 338--367
month: aug
monthnumber: 8
year: 2011
CODEN: HIMADS
ISSN: 0315-0860 (print), 1090-249X (electronic) OR 03150860 (print), 1090249X (electronic)
ISSNL: 0315-0860 OR 03150860
bibdate: Wed Jun 26 06:21:13 MDT 2013
bibtimestamp: 2013.06.26 06:21:13 MDT
URL: http://www.sciencedirect.com/science/article/pii/S0315086010000546
fjournal: Historia Mathematica
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03150860
rawauthor: Bo G{\"o}ran Johansson
rawtitle: Cube root extraction in medieval mathematics
entry:
@Article{Johansson:2011:CRE,
  author =       "Bo G{\"o}ran Johansson",
  title =        "Cube root extraction in medieval mathematics",
  journal =      j-HIST-MATH,
  volume =       "38",
  number =       "3",
  pages =        "338--367",
  month =        aug,
  year =         "2011",
  CODEN =        "HIMADS",
  ISSN =         "0315-0860 (print), 1090-249X (electronic)",
  ISSN-L =       "0315-0860",
  bibdate =      "Wed Jun 26 06:21:13 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/histmath.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0315086010000546",
  acknowledgement = ack-nhfb,
  fjournal =     "Historia Mathematica",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03150860",
}


bibtype: article
filename: elefunt.bib
label: Knessl:2011:EAF
author: Charles Knessl and Mark W. Coffey
title: An effective asymptotic formula for the Stieltjes constants
journal: j-MATH-COMPUT
volume: 80
number: 273
pages: 379--386
month: jan
monthnumber: 1
year: 2011
CODEN: MCMPAF
DOI: https://doi.org/10.1090/S0025-5718-2010-02390-7
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Wed Oct 13 16:46:42 MDT 2010
bibsource: http://www.ams.org/mcom/2011-80-273; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.13 16:46:42 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Charles Knessl and Mark W. Coffey
rawtitle: An effective asymptotic formula for the {Stieltjes} constants
URL:
http://www.ams.org/journals/mcom/2011-80-273/S0025-5718-2010-02390-7/home.html; http://www.ams.org/journals/mcom/2011-80-273/S0025-5718-2010-02390-7/S0025-5718-2010-02390-7.pdf

abstract:
The Stieltjes constants $ gamma _k $ appear in the coefficients in the regular part of the Laurent expansion of the Riemann zeta function $ zeta (s) $ about its only pole at $ s = 1 $. We present an asymptotic expression for $ gamma _k $ for $ k gg 1 $. This form encapsulates both the leading rate of growth and the oscillations with $k$. Furthermore, our result is effective for computation, consistently in close agreement (for both magnitude and sign) for even moderate values of $k$. Comparison to some earlier work is made.

rawabstract:
The Stieltjes constants $ \gamma_k $ appear in the coefficients in the regular part of the Laurent expansion of the Riemann zeta function $ \zeta (s) $ about its only pole at $ s = 1 $. We present an asymptotic expression for $ \gamma_k $ for $ k \gg 1 $. This form encapsulates both the leading rate of growth and the oscillations with $k$. Furthermore, our result is effective for computation, consistently in close agreement (for both magnitude and sign) for even moderate values of $k$. Comparison to some earlier work is made.

entry:
@Article{Knessl:2011:EAF,
  author =       "Charles Knessl and Mark W. Coffey",
  title =        "An effective asymptotic formula for the {Stieltjes}
                 constants",
  journal =      j-MATH-COMPUT,
  volume =       "80",
  number =       "273",
  pages =        "379--386",
  month =        jan,
  year =         "2011",
  CODEN =        "MCMPAF",
  DOI =          "https://doi.org/10.1090/S0025-5718-2010-02390-7",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Wed Oct 13 16:46:42 MDT 2010",
  bibsource =    "http://www.ams.org/mcom/2011-80-273;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.ams.org/journals/mcom/2011-80-273/S0025-5718-2010-02390-7/home.html;
                 http://www.ams.org/journals/mcom/2011-80-273/S0025-5718-2010-02390-7/S0025-5718-2010-02390-7.pdf",
  abstract =     "The Stieltjes constants $ \gamma_k $ appear in the
                 coefficients in the regular part of the Laurent
                 expansion of the Riemann zeta function $ \zeta (s) $
                 about its only pole at $ s = 1 $. We present an
                 asymptotic expression for $ \gamma_k $ for $ k \gg 1 $.
                 This form encapsulates both the leading rate of growth
                 and the oscillations with $k$. Furthermore, our result
                 is effective for computation, consistently in close
                 agreement (for both magnitude and sign) for even
                 moderate values of $k$. Comparison to some earlier work
                 is made.",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Kodama:2011:AMC
author: Masao Kodama
title: Algorithm 912: a Module for Calculating Cylindrical Functions of Complex Order and Complex Argument
journal: j-TOMS
volume: 37
number: 4
pages: 47:1--47:25
month: feb
monthnumber: 2
year: 2011
CODEN: ACMSCU
DOI: https://doi.org/10.1145/1916461.1916471
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Tue Mar 1 16:05:18 MST 2011
bibtimestamp: 2011.03.01 16:05:18 MST
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
articleno: 47
journalURL: https://dl.acm.org/loi/toms
rawauthor: Masao Kodama
abstract:
The present algorithm provides a module for calculating the cylindrical functions $ J_nu (z) $, $ Y_nu (z) $, $ H_nu (1)(z) $, and $ H_nu (2)(z) $, where the order $ nu $ is complex and the complex argument $z$ satisfies $ - pi < arg z leq pi $. The algorithm is written in Fortran 90 and calculates the functions using real and complex numbers of any intrinsic data type whose kind type parameter the user's Fortran system accepts. The methods of calculating the functions are based on two kinds of series expansions and numerical integration. Wronskian tests examine the functional values computed by this algorithm with double precision at 4,100,625 pseudorandom test points in the region $ | Re nu | leq 60 $, $ | Im nu | leq 60 $, $ | Re z| leq 300 $, $ | Im z| leq 300 $.

rawabstract:
The present algorithm provides a module for calculating the cylindrical functions $ J_\nu (z) $, $ Y_\nu (z) $, $ H_{\nu (1)}(z) $, and $ H_{\nu (2)}(z) $, where the order $ \nu $ is complex and the complex argument $z$ satisfies $ - \pi < \arg z \leq \pi $. The algorithm is written in Fortran 90 and calculates the functions using real and complex numbers of any intrinsic data type whose kind type parameter the user's Fortran system accepts. The methods of calculating the functions are based on two kinds of series expansions and numerical integration. Wronskian tests examine the functional values computed by this algorithm with double precision at 4,100,625 pseudorandom test points in the region $ | \Re \nu | \leq 60 $, $ | \Im \nu | \leq 60 $, $ | \Re z| \leq 300 $, $ | \Im z| \leq 300 $.

rawtitle:
{Algorithm 912}: a Module for Calculating Cylindrical Functions of Complex Order and Complex Argument

entry:
@Article{Kodama:2011:AMC,
  author =       "Masao Kodama",
  title =        "{Algorithm 912}: a Module for Calculating Cylindrical
                 Functions of Complex Order and Complex Argument",
  journal =      j-TOMS,
  volume =       "37",
  number =       "4",
  pages =        "47:1--47:25",
  month =        feb,
  year =         "2011",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1916461.1916471",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 1 16:05:18 MST 2011",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The present algorithm provides a module for
                 calculating the cylindrical functions $ J_\nu (z) $, $
                 Y_\nu (z) $, $ H_{\nu (1)}(z) $, and $ H_{\nu (2)}(z)
                 $, where the order $ \nu $ is complex and the complex
                 argument $z$ satisfies $ - \pi < \arg z \leq \pi $. The
                 algorithm is written in Fortran 90 and calculates the
                 functions using real and complex numbers of any
                 intrinsic data type whose kind type parameter the
                 user's Fortran system accepts. The methods of
                 calculating the functions are based on two kinds of
                 series expansions and numerical integration. Wronskian
                 tests examine the functional values computed by this
                 algorithm with double precision at 4,100,625
                 pseudorandom test points in the region $ | \Re \nu |
                 \leq 60 $, $ | \Im \nu | \leq 60 $, $ | \Re z| \leq 300
                 $, $ | \Im z| \leq 300 $.",
  acknowledgement = ack-nhfb,
  articleno =    "47",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: article
filename: elefunt.bib
label: Kormanyos:2011:APC
author: Christopher Kormanyos
title: Algorithm 910: a Portable C++ Multiple-Precision System for Special-Function Calculations
journal: j-TOMS
volume: 37
number: 4
pages: 45:1--45:27
month: feb
monthnumber: 2
year: 2011
CODEN: ACMSCU
DOI: https://doi.org/10.1145/1916461.1916469
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Tue Mar 1 16:05:18 MST 2011
bibtimestamp: 2011.03.01 16:05:18 MST
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
articleno: 45
journalURL: https://dl.acm.org/loi/toms
rawauthor: Christopher Kormanyos
rawtitle: {Algorithm 910}: a Portable {C++} Multiple-Precision System for Special-Function Calculations
abstract:
This article presents a portable C++ system for multiple precision calculations of special functions called tt e_float. It has an extendable architecture with a uniform C++ layer which can be used with any suitably prepared MP type. The system implements many high-precision special functions and extends some of these to very large parameter ranges. It supports calculations with 30 ldots 300 decimal digits of precision. Interoperabilities with Microsoft's CLR, Python, and Mathematicareg are supported. The tt e_float system and its usage are described in detail. Implementation notes, testing results, and performance measurements are provided.

rawabstract:
This article presents a portable C++ system for multiple precision calculations of special functions called {\tt e\_float}. It has an extendable architecture with a uniform C++ layer which can be used with any suitably prepared MP type. The system implements many high-precision special functions and extends some of these to very large parameter ranges. It supports calculations with 30 \ldots{} 300 decimal digits of precision. Interoperabilities with Microsoft's CLR, Python, and Mathematica{\reg} are supported. The {\tt e\_float} system and its usage are described in detail. Implementation notes, testing results, and performance measurements are provided.

entry:
@Article{Kormanyos:2011:APC,
  author =       "Christopher Kormanyos",
  title =        "{Algorithm 910}: a Portable {C++} Multiple-Precision
                 System for Special-Function Calculations",
  journal =      j-TOMS,
  volume =       "37",
  number =       "4",
  pages =        "45:1--45:27",
  month =        feb,
  year =         "2011",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1916461.1916469",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 1 16:05:18 MST 2011",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "This article presents a portable C++ system for
                 multiple precision calculations of special functions
                 called {\tt e\_float}. It has an extendable
                 architecture with a uniform C++ layer which can be used
                 with any suitably prepared MP type. The system
                 implements many high-precision special functions and
                 extends some of these to very large parameter ranges.
                 It supports calculations with 30 \ldots{} 300 decimal
                 digits of precision. Interoperabilities with
                 Microsoft's CLR, Python, and Mathematica{\reg} are
                 supported. The {\tt e\_float} system and its usage are
                 described in detail. Implementation notes, testing
                 results, and performance measurements are provided.",
  acknowledgement = ack-nhfb,
  articleno =    "45",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: article
filename: elefunt.bib
label: Lopez-Benitez:2011:VAA
author: Miguel Lopez-Benitez and Fernando Casadevall
title: Versatile, Accurate, and Analytically Tractable Approximation for the Gaussian $Q$-Function
journal: j-IEEE-TRANS-COMM
volume: 59
number: 4
pages: 917--922
month: apr
monthnumber: 4
year: 2011
CODEN: IECMBT
DOI: https://doi.org/10.1109/tcomm.2011.012711.100105
ISSN: 0090-6778 (print), 1558-0857 (electronic) OR 00906778 (print), 15580857 (electronic)
ISSNL: 0090-6778 OR 00906778
bibdate: Sat Dec 16 17:01:00 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.12.16 17:01:00 ???
URL: http://ieeexplore.ieee.org/document/5706433/
fjournal: IEEE Transactions on Communications
acknowledgement: ack-nhfb
rawauthor: Miguel L{\"o}pez-Benitez and Fernando Casadevall
rawtitle: Versatile, Accurate, and Analytically Tractable Approximation for the {Gaussian} {$Q$}-Function
entry:
@Article{Lopez-Benitez:2011:VAA,
  author =       "Miguel L{\"o}pez-Benitez and Fernando Casadevall",
  title =        "Versatile, Accurate, and Analytically Tractable
                 Approximation for the {Gaussian} {$Q$}-Function",
  journal =      j-IEEE-TRANS-COMM,
  volume =       "59",
  number =       "4",
  pages =        "917--922",
  month =        apr,
  year =         "2011",
  CODEN =        "IECMBT",
  DOI =          "https://doi.org/10.1109/tcomm.2011.012711.100105",
  ISSN =         "0090-6778 (print), 1558-0857 (electronic)",
  ISSN-L =       "0090-6778",
  bibdate =      "Sat Dec 16 17:01:00 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://ieeexplore.ieee.org/document/5706433/",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Communications",
}


bibtype: article
filename: elefunt.bib
label: Mortici:2011:IAF
author: Cristinel Mortici
title: Improved asymptotic formulas for the gamma function
journal: j-COMPUT-MATH-APPL
volume: 61
number: 11
pages: 3364--3369
month: jun
monthnumber: 6
year: 2011
CODEN: CMAPDK
DOI: https://doi.org/10.1016/j.camwa.2011.04.036
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Wed Mar 1 21:50:47 MST 2017
bibtimestamp: 2017.03.01 21:50:47 MST
URL: http://www.sciencedirect.com/science/article/pii/S0898122111003373
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/08981221
rawauthor: Cristinel Mortici
rawtitle: Improved asymptotic formulas for the gamma function
bibsource:
https://www.math.utah.edu/pub/tex/bib/computmathappl2010.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Mortici:2011:IAF,
  author =       "Cristinel Mortici",
  title =        "Improved asymptotic formulas for the gamma function",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "61",
  number =       "11",
  pages =        "3364--3369",
  month =        jun,
  year =         "2011",
  CODEN =        "CMAPDK",
  DOI =          "https://doi.org/10.1016/j.camwa.2011.04.036",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 21:50:47 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0898122111003373",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}


bibtype: inproceedings
filename: elefunt.bib
label: Nannarelli:2011:RCD
author: Alberto Nannarelli
title: Radix-16 Combined Division and Square Root Unit
crossref: Schwarz:2011:PIS
pages: 169--176
year: 2011
DOI: https://doi.org/10.1109/ARITH.2011.30
bibdate: Sat Aug 20 09:00:00 MDT 2011
bibtimestamp: 2011.08.20 09:00:00 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992122
keywords: ARITH-20; sqrt(x); square root
acknowledgement: ack-nhfb
rawauthor: Alberto Nannarelli
rawtitle: Radix-16 Combined Division and Square Root Unit
entry:
@InProceedings{Nannarelli:2011:RCD,
  author =       "Alberto Nannarelli",
  title =        "Radix-16 Combined Division and Square Root Unit",
  crossref =     "Schwarz:2011:PIS",
  pages =        "169--176",
  year =         "2011",
  DOI =          "https://doi.org/10.1109/ARITH.2011.30",
  bibdate =      "Sat Aug 20 09:00:00 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992122",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-20; sqrt(x); square root",
}


bibtype: article
filename: elefunt.bib
label: Paszkowski:2011:UMC
author: Stefan Paszkowski
title: Untypical methods of convergence acceleration
journal: j-NUMER-ALGORITHMS
volume: 56
number: 2
pages: 185--209
year: 2011
CODEN: NUALEG
ISSN: 1017-1398 (print), 1572-9265 (electronic) OR 10171398 (print), 15729265 (electronic)
ISSNL: 1017-1398 OR 10171398
MRclass: 65B10 (33C20 33E05 41Axx)
MRnumber: MR2755669
bibdate: Thu Dec 01 09:27:45 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2011.12.01 09:27:45 ???
fjournal: Numerical Algorithms
keywords: convergence acceleration
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/11075
rawauthor: Stefan Paszkowski
rawtitle: Untypical methods of convergence acceleration
entry:
@Article{Paszkowski:2011:UMC,
  author =       "Stefan Paszkowski",
  title =        "Untypical methods of convergence acceleration",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "56",
  number =       "2",
  pages =        "185--209",
  month =        "????",
  year =         "2011",
  CODEN =        "NUALEG",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  MRclass =      "65B10 (33C20 33E05 41Axx)",
  MRnumber =     "MR2755669",
  bibdate =      "Thu Dec 01 09:27:45 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
  keywords =     "convergence acceleration",
}


bibtype: article
filename: elefunt.bib
label: Pawellek:2011:GJE
author: Michael Pawellek
title: On a generalization of Jacobi's elliptic functions and the double sine--Gordon kink chain
journal: j-J-MATH-PHYS
volume: 52
number: 11
pages: 113701
month: nov
monthnumber: 11
year: 2011
CODEN: JMAPAQ
DOI: https://doi.org/10.1063/1.3656873
ISSNL: 0022-2488 OR 00222488
bibdate: Wed Jan 4 08:04:23 MST 2012
bibtimestamp: 2012.01.04 08:04:23 MST
URL: http://jmp.aip.org/resource/1/jmapaq/v52/i11/p113701_s1
fjournal: Journal of Mathematical Physics
acknowledgement: ack-nhfb
journalURL: http://jmp.aip.org/
onlinedate: 4 November 2011
rawauthor: Michael Pawellek
rawtitle: On a generalization of {Jacobi}'s elliptic functions and the double {sine--Gordon} kink chain
bibsource:
http://www.aip.org/ojs/jmp.html; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jmathphys2010.bib

entry:
@Article{Pawellek:2011:GJE,
  author =       "Michael Pawellek",
  title =        "On a generalization of {Jacobi}'s elliptic functions
                 and the double {sine--Gordon} kink chain",
  journal =      j-J-MATH-PHYS,
  volume =       "52",
  number =       "11",
  pages =        "113701",
  month =        nov,
  year =         "2011",
  CODEN =        "JMAPAQ",
  DOI =          "https://doi.org/10.1063/1.3656873",
  ISSN =         "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
  ISSN-L =       "0022-2488",
  bibdate =      "Wed Jan 4 08:04:23 MST 2012",
  bibsource =    "http://www.aip.org/ojs/jmp.html;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jmathphys2010.bib",
  URL =          "http://jmp.aip.org/resource/1/jmapaq/v52/i11/p113701_s1",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Physics",
  journal-URL =  "http://jmp.aip.org/",
  onlinedate =   "4 November 2011",
  pagecount =    "18",
}


bibtype: article
filename: elefunt.bib
label: Pegoraro:2011:ECV
author: Vincent Pegoraro and Philipp Slusallek
title: On the Evaluation of the Complex-Valued Exponential Integral
journal: j-J-GRAPHICS-GPU-GAME-TOOLS
volume: 15
number: 3
pages: 183--198
year: 2011
DOI: https://doi.org/10.1080/2151237X.2011.617177
ISSN: 2151-237X OR 2151237X
bibdate: Wed Dec 14 10:31:39 MST 2011
bibtimestamp: 2011.12.14 10:31:39 MST
acknowledgement: ack-nhfb
journalURL: http://www.tandfonline.com/loi/ujgt20
onlinedate: 21 Oct 2011
rawauthor: Vincent Pegoraro and Philipp Slusallek
rawtitle: On the Evaluation of the Complex-Valued Exponential Integral
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jgraphtools.bib

abstract:
Although its applications span a broad scope of scientific fields ranging from applied physics to computer graphics, the exponential integral is a nonelementary special function available in specialized software packages but not in standard libraries, consequently requiring custom implementations on most platforms. In this paper, we provide a concise and comprehensive description of how to evaluate the complex-valued exponential integral. We first introduce some theoretical background on the main characteristics of the function, and outline available third-party proprietary implementations. We then provide an analysis of the various known representations of the function and present an effective algorithm allowing the computation of results within a desired accuracy, together with the corresponding pseudocode in order to facilitate portability onto various systems. An application to the calculation of the closed-form solution to single light scattering in homogeneous participating media illustrates the practical benefits of the provided implementation with the hope that, in the long term, the latter will contribute to standardizing the availability of the complex-valued exponential integral on graphics platforms.

rawabstract:
Although its applications span a broad scope of scientific fields ranging from applied physics to computer graphics, the exponential integral is a nonelementary special function available in specialized software packages but not in standard libraries, consequently requiring custom implementations on most platforms. In this paper, we provide a concise and comprehensive description of how to evaluate the complex-valued exponential integral. We first introduce some theoretical background on the main characteristics of the function, and outline available third-party proprietary implementations. We then provide an analysis of the various known representations of the function and present an effective algorithm allowing the computation of results within a desired accuracy, together with the corresponding pseudocode in order to facilitate portability onto various systems. An application to the calculation of the closed-form solution to single light scattering in homogeneous participating media illustrates the practical benefits of the provided implementation with the hope that, in the long term, the latter will contribute to standardizing the availability of the complex-valued exponential integral on graphics platforms.

entry:
@Article{Pegoraro:2011:ECV,
  author =       "Vincent Pegoraro and Philipp Slusallek",
  title =        "On the Evaluation of the Complex-Valued Exponential
                 Integral",
  journal =      j-J-GRAPHICS-GPU-GAME-TOOLS,
  volume =       "15",
  number =       "3",
  pages =        "183--198",
  year =         "2011",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/2151237X.2011.617177",
  ISSN =         "2151-237X",
  bibdate =      "Wed Dec 14 10:31:39 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jgraphtools.bib",
  abstract =     "Although its applications span a broad scope of
                 scientific fields ranging from applied physics to
                 computer graphics, the exponential integral is a
                 nonelementary special function available in specialized
                 software packages but not in standard libraries,
                 consequently requiring custom implementations on most
                 platforms. In this paper, we provide a concise and
                 comprehensive description of how to evaluate the
                 complex-valued exponential integral. We first introduce
                 some theoretical background on the main characteristics
                 of the function, and outline available third-party
                 proprietary implementations. We then provide an
                 analysis of the various known representations of the
                 function and present an effective algorithm allowing
                 the computation of results within a desired accuracy,
                 together with the corresponding pseudocode in order to
                 facilitate portability onto various systems. An
                 application to the calculation of the closed-form
                 solution to single light scattering in homogeneous
                 participating media illustrates the practical benefits
                 of the provided implementation with the hope that, in
                 the long term, the latter will contribute to
                 standardizing the availability of the complex-valued
                 exponential integral on graphics platforms.",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://www.tandfonline.com/loi/ujgt20",
  onlinedate =   "21 Oct 2011",
}


bibtype: article
filename: elefunt.bib
label: Shi:2011:AEA
author: Qinghua Shi and Y. Karasawa
journal: j-IEEE-COMMUN-LET
volume: 15
number: 5
pages: 479--481
month: may
monthnumber: 5
year: 2011
CODEN: ICLEF6
DOI: https://doi.org/10.1109/lcomm.2011.032111.102440
ISSN: 1089-7798 (print), 1558-2558 (electronic) OR 10897798 (print), 15582558 (electronic)
ISSNL: 1089-7798 OR 10897798
bibdate: Sat Dec 16 17:32:51 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.12.16 17:32:51 ???
URL: http://ieeexplore.ieee.org/document/5740503/
fjournal: IEEE Communications Letters
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4234
rawauthor: Qinghua Shi and Y. Karasawa
title:
An Accurate and Efficient Approximation to the Gaussian $Q$-Function and its Applications in Performance Analysis in Nakagami-$m$ Fading

rawtitle:
An Accurate and Efficient Approximation to the {Gaussian} {$Q$}-Function and its Applications in Performance Analysis in {Nakagami}-$m$ Fading

entry:
@Article{Shi:2011:AEA,
  author =       "Qinghua Shi and Y. Karasawa",
  title =        "An Accurate and Efficient Approximation to the
                 {Gaussian} {$Q$}-Function and its Applications in
                 Performance Analysis in {Nakagami}-$m$ Fading",
  journal =      j-IEEE-COMMUN-LET,
  volume =       "15",
  number =       "5",
  pages =        "479--481",
  month =        may,
  year =         "2011",
  CODEN =        "ICLEF6",
  DOI =          "https://doi.org/10.1109/lcomm.2011.032111.102440",
  ISSN =         "1089-7798 (print), 1558-2558 (electronic)",
  ISSN-L =       "1089-7798",
  bibdate =      "Sat Dec 16 17:32:51 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://ieeexplore.ieee.org/document/5740503/",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Communications Letters",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4234",
}


bibtype: article
filename: elefunt.bib
label: Smith:2011:AMP
author: David M. Smith
title: Algorithm 911: Multiple-Precision Exponential Integral and Related Functions
journal: j-TOMS
volume: 37
number: 4
pages: 46:1--46:16
month: feb
monthnumber: 2
year: 2011
CODEN: ACMSCU
DOI: https://doi.org/10.1145/1916461.1916470
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Tue Mar 1 16:05:18 MST 2011
bibtimestamp: 2011.03.01 16:05:18 MST
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
articleno: 46
journalURL: https://dl.acm.org/loi/toms
rawauthor: David M. Smith
rawtitle: {Algorithm 911}: Multiple-Precision Exponential Integral and Related Functions
abstract:
This article describes a collection of Fortran-95 routines for evaluating the exponential integral function, error function, sine and cosine integrals, Fresnel integrals, Bessel functions, and related mathematical special functions using the FM multiple-precision arithmetic package.

rawabstract:
This article describes a collection of Fortran-95 routines for evaluating the exponential integral function, error function, sine and cosine integrals, Fresnel integrals, Bessel functions, and related mathematical special functions using the FM multiple-precision arithmetic package.

entry:
@Article{Smith:2011:AMP,
  author =       "David M. Smith",
  title =        "{Algorithm 911}: Multiple-Precision Exponential
                 Integral and Related Functions",
  journal =      j-TOMS,
  volume =       "37",
  number =       "4",
  pages =        "46:1--46:16",
  month =        feb,
  year =         "2011",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1916461.1916470",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 1 16:05:18 MST 2011",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "This article describes a collection of Fortran-95
                 routines for evaluating the exponential integral
                 function, error function, sine and cosine integrals,
                 Fresnel integrals, Bessel functions, and related
                 mathematical special functions using the FM
                 multiple-precision arithmetic package.",
  acknowledgement = ack-nhfb,
  articleno =    "46",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: article
filename: elefunt.bib
label: Srivastava:2011:ADZ
author: H. M. Srivastava and Jian-Rong Zhou and Zhi-Gang Wang
journal: j-MATH-COMPUT
volume: 80
number: 275
pages: 1769--1784
month: jul
monthnumber: 7
year: 2011
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Mon Apr 18 06:32:30 MDT 2011
bibtimestamp: 2011.04.18 06:32:30 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: H. M. Srivastava and Jian-Rong Zhou and Zhi-Gang Wang
title:
Asymptotic distributions of the zeros of certain classes of hypergeometric functions and polynomials

bibsource:
http://www.ams.org/mcom/2011-80-275; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp2010.bib

URL:
http://www.ams.org/journals/mcom/2011-80-275/S0025-5718-2011-02409-9/home.html; http://www.ams.org/journals/mcom/2011-80-275/S0025-5718-2011-02409-9/S0025-5718-2011-02409-9.pdf

rawtitle:
Asymptotic distributions of the zeros of certain classes of hypergeometric functions and polynomials

entry:
@Article{Srivastava:2011:ADZ,
  author =       "H. M. Srivastava and Jian-Rong Zhou and Zhi-Gang
                 Wang",
  title =        "Asymptotic distributions of the zeros of certain
                 classes of hypergeometric functions and polynomials",
  journal =      j-MATH-COMPUT,
  volume =       "80",
  number =       "275",
  pages =        "1769--1784",
  month =        jul,
  year =         "2011",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Mon Apr 18 06:32:30 MDT 2011",
  bibsource =    "http://www.ams.org/mcom/2011-80-275;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp2010.bib",
  URL =          "http://www.ams.org/journals/mcom/2011-80-275/S0025-5718-2011-02409-9/home.html;
                 http://www.ams.org/journals/mcom/2011-80-275/S0025-5718-2011-02409-9/S0025-5718-2011-02409-9.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Strollo:2011:EFH
author: Antonio Giuseppe Maria Strollo and Davide De Caro and Nicola Petra
title: Elementary Functions Hardware Implementation Using Constrained Piecewise-Polynomial Approximations
journal: j-IEEE-TRANS-COMPUT
volume: 60
pages: 418--432
year: 2011
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.2010.127
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sun Feb 20 19:10:07 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2011.02.20 19:10:07 ???
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Antonio Giuseppe Maria Strollo and Davide {De Caro} and Nicola Petra
rawtitle: Elementary Functions Hardware Implementation Using Constrained Piecewise-Polynomial Approximations
abstract:
A novel technique for designing piecewise-polynomial interpolators for hardware implementation of elementary functions is investigated in this paper. In the proposed approach, the interval where the function is approximated is subdivided in equal length segments and two adjacent segments are grouped in a segment pair. Suitable constraints are then imposed between the coefficients of the two interpolating polynomials in each segment pair. This allows reducing the total number of stored coefficients. It is found that the increase in the approximation error due to constraints between polynomial coefficients can easily be overcome by increasing the fractional bits of the coefficients. Overall, compared with standard unconstrained piecewise-polynomial approximation having the same accuracy, the proposed method results in a considerable advantage in terms of the size of the lookup table needed to store polynomial coefficients. The calculus of the coefficients of constrained polynomials and the optimization of coefficients bit width is also investigated in this paper. Results for several elementary functions and target precision ranging from 12 to 42 bits are presented. The paper also presents VLSI implementation results, targeting a 90 nm CMOS technology, and using both direct and Horner architectures for constrained degree-1, degree-2, and degree-3 approximations.

keywords:
computer arithmetic; elementary functions; min-max approximation; polynomial approximation; VLSI systems.

rawabstract:
A novel technique for designing piecewise-polynomial interpolators for hardware implementation of elementary functions is investigated in this paper. In the proposed approach, the interval where the function is approximated is subdivided in equal length segments and two adjacent segments are grouped in a segment pair. Suitable constraints are then imposed between the coefficients of the two interpolating polynomials in each segment pair. This allows reducing the total number of stored coefficients. It is found that the increase in the approximation error due to constraints between polynomial coefficients can easily be overcome by increasing the fractional bits of the coefficients. Overall, compared with standard unconstrained piecewise-polynomial approximation having the same accuracy, the proposed method results in a considerable advantage in terms of the size of the lookup table needed to store polynomial coefficients. The calculus of the coefficients of constrained polynomials and the optimization of coefficients bit width is also investigated in this paper. Results for several elementary functions and target precision ranging from 12 to 42 bits are presented. The paper also presents VLSI implementation results, targeting a 90 nm CMOS technology, and using both direct and Horner architectures for constrained degree-1, degree-2, and degree-3 approximations.

entry:
@Article{Strollo:2011:EFH,
  author =       "Antonio Giuseppe Maria Strollo and Davide {De Caro}
                 and Nicola Petra",
  title =        "Elementary Functions Hardware Implementation Using
                 Constrained Piecewise-Polynomial Approximations",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "60",
  pages =        "418--432",
  year =         "2011",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2010.127",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Feb 20 19:10:07 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "A novel technique for designing piecewise-polynomial
                 interpolators for hardware implementation of elementary
                 functions is investigated in this paper. In the
                 proposed approach, the interval where the function is
                 approximated is subdivided in equal length segments and
                 two adjacent segments are grouped in a segment pair.
                 Suitable constraints are then imposed between the
                 coefficients of the two interpolating polynomials in
                 each segment pair. This allows reducing the total
                 number of stored coefficients. It is found that the
                 increase in the approximation error due to constraints
                 between polynomial coefficients can easily be overcome
                 by increasing the fractional bits of the coefficients.
                 Overall, compared with standard unconstrained
                 piecewise-polynomial approximation having the same
                 accuracy, the proposed method results in a considerable
                 advantage in terms of the size of the lookup table
                 needed to store polynomial coefficients. The calculus
                 of the coefficients of constrained polynomials and the
                 optimization of coefficients bit width is also
                 investigated in this paper. Results for several
                 elementary functions and target precision ranging from
                 12 to 42 bits are presented. The paper also presents
                 VLSI implementation results, targeting a 90 nm CMOS
                 technology, and using both direct and Horner
                 architectures for constrained degree-1, degree-2, and
                 degree-3 approximations.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "computer arithmetic; elementary functions; min-max
                 approximation; polynomial approximation; VLSI
                 systems.",
}


bibtype: inproceedings
filename: elefunt.bib
label: Tang:2011:TCT
author: Ping Tak Peter Tang and J. Adam Butts and Ron O. Dror and David E. Shaw
crossref: Schwarz:2011:PIS
pages: 159--168
year: 2011
DOI: https://doi.org/10.1109/ARITH.2011.29
bibdate: Sat Aug 20 09:00:00 MDT 2011
bibtimestamp: 2011.08.20 09:00:00 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992121
keywords: ARITH-20; reciprocal square root; rsqrt(x)
acknowledgement: ack-nhfb
rawauthor: Ping Tak Peter Tang and J. Adam Butts and Ron O. Dror and David E. Shaw
title:
Tight Certification Techniques for Digit-by-Rounding Algorithms with Application to a New $ 1 / sqrt x $ Design

rawtitle:
Tight Certification Techniques for Digit-by-Rounding Algorithms with Application to a New $ 1 / \sqrt {x} $ Design

entry:
@InProceedings{Tang:2011:TCT,
  author =       "Ping Tak Peter Tang and J. Adam Butts and Ron O. Dror
                 and David E. Shaw",
  title =        "Tight Certification Techniques for Digit-by-Rounding
                 Algorithms with Application to a New $ 1 / \sqrt {x} $
                 Design",
  crossref =     "Schwarz:2011:PIS",
  pages =        "159--168",
  year =         "2011",
  DOI =          "https://doi.org/10.1109/ARITH.2011.29",
  bibdate =      "Sat Aug 20 09:00:00 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992121",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-20; reciprocal square root; rsqrt(x)",
}


bibtype: article
filename: elefunt.bib
label: Trudgian:2011:ITM
author: Timothy Trudgian
title: Improvements to Turing's method
journal: j-MATH-COMPUT
volume: 80
number: 276
pages: 2259--2279
month: oct
monthnumber: 10
year: 2011
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Mon Oct 24 10:33:34 MDT 2011
bibtimestamp: 2011.10.24 10:33:34 MDT
note: See cite Turing:1953:SCR,Lehman:1970:DZR.
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Timothy Trudgian
rawnote: See \cite{Turing:1953:SCR,Lehman:1970:DZR}.
rawtitle: Improvements to {Turing}'s method
bibsource:
http://www.ams.org/mcom/2011-80-276; https://www.math.utah.edu/pub/bibnet/authors/t/turing-alan-mathison.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp2010.bib

URL:
http://www.ams.org/journals/mcom/2011-80-276/S0025-5718-2011-02470-1/home.html; http://www.ams.org/journals/mcom/2011-80-276/S0025-5718-2011-02470-1/S0025-5718-2011-02470-1.pdf; http://www.ams.org/mathscinet-getitem?mr=2813359

abstract:
This article improves the estimate of the size of the definite integral of $ S(t) $, the argument of the Riemann zeta-function. The primary application of this improvement is Turing's Method for the Riemann zeta-function. Analogous improvements are given for the arguments of Dirichlet $L$-functions and of Dedekind zeta-functions.

rawabstract:
This article improves the estimate of the size of the definite integral of {$ S(t) $}, the argument of the Riemann zeta-function. The primary application of this improvement is Turing's Method for the Riemann zeta-function. Analogous improvements are given for the arguments of Dirichlet {$L$}-functions and of Dedekind zeta-functions.

entry:
@Article{Trudgian:2011:ITM,
  author =       "Timothy Trudgian",
  title =        "Improvements to {Turing}'s method",
  journal =      j-MATH-COMPUT,
  volume =       "80",
  number =       "276",
  pages =        "2259--2279",
  month =        oct,
  year =         "2011",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Mon Oct 24 10:33:34 MDT 2011",
  bibsource =    "http://www.ams.org/mcom/2011-80-276;
                 https://www.math.utah.edu/pub/bibnet/authors/t/turing-alan-mathison.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp2010.bib",
  note =         "See \cite{Turing:1953:SCR,Lehman:1970:DZR}.",
  URL =          "http://www.ams.org/journals/mcom/2011-80-276/S0025-5718-2011-02470-1/home.html;
                 http://www.ams.org/journals/mcom/2011-80-276/S0025-5718-2011-02470-1/S0025-5718-2011-02470-1.pdf;
                 http://www.ams.org/mathscinet-getitem?mr=2813359",
  abstract =     "This article improves the estimate of the size of the
                 definite integral of {$ S(t) $}, the argument of the
                 Riemann zeta-function. The primary application of this
                 improvement is Turing's Method for the Riemann
                 zeta-function. Analogous improvements are given for the
                 arguments of Dirichlet {$L$}-functions and of Dedekind
                 zeta-functions.",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: VanDeun:2011:RIC
author: Joris Van Deun and Lloyd N. Trefethen
title: A robust implementation of the Caratheodory-Fejer method for rational approximation
journal: j-BIT-NUM-MATH
volume: 51
pages: ??--??
year: 2011
CODEN: BITTEL, NBITAB
DOI: https://doi.org/10.1007/s10543-011-0331-7
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
ISSNL: 0006-3835 OR 00063835
bibdate: Thu Sep 29 07:17:26 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2011.09.29 07:17:26 ???
URL: http://www.springerlink.com/content/ag2514840142707r/
keywords: Caratheodory-Fejer approximation; Chebfun; Near-best rational approximation
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10543
onlinedate: 04 May 2011
rawauthor: Joris {Van Deun} and Lloyd N. Trefethen
rawtitle: A robust implementation of the {Carath{\'e}odory-Fej{\'e}r} method for rational approximation
abstract:
Best rational approximations are notoriously difficult to compute. However, the difference between the best rational approximation to a function and its Caratheodory-Fejer (CF) approximation is often so small as to be negligible in practice, while CF approximations are far easier to compute. We present a robust and fast implementation of this method in the Chebfun software system and illustrate its use with several examples. Our implementation handles both polynomial and rational approximation and substantially improves upon earlier published software.

rawabstract:
Best rational approximations are notoriously difficult to compute. However, the difference between the best rational approximation to a function and its Carath{\'e}odory-Fej{\'e}r (CF) approximation is often so small as to be negligible in practice, while CF approximations are far easier to compute. We present a robust and fast implementation of this method in the Chebfun software system and illustrate its use with several examples. Our implementation handles both polynomial and rational approximation and substantially improves upon earlier published software.

entry:
@Article{VanDeun:2011:RIC,
  author =       "Joris {Van Deun} and Lloyd N. Trefethen",
  title =        "A robust implementation of the
                 {Carath{\'e}odory-Fej{\'e}r} method for rational
                 approximation",
  journal =      j-BIT-NUM-MATH,
  volume =       "51",
  number =       "??",
  pages =        "??--??",
  month =        "????",
  year =         "2011",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/s10543-011-0331-7",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Thu Sep 29 07:17:26 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.springerlink.com/content/ag2514840142707r/",
  abstract =     "Best rational approximations are notoriously difficult
                 to compute. However, the difference between the best
                 rational approximation to a function and its
                 Carath{\'e}odory-Fej{\'e}r (CF) approximation is often
                 so small as to be negligible in practice, while CF
                 approximations are far easier to compute. We present a
                 robust and fast implementation of this method in the
                 Chebfun software system and illustrate its use with
                 several examples. Our implementation handles both
                 polynomial and rational approximation and substantially
                 improves upon earlier published software.",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "Carath{\'e}odory-Fej{\'e}r approximation; Chebfun;
                 Near-best rational approximation",
  onlinedate =   "04 May 2011",
}


bibtype: article
filename: elefunt.bib
label: Veling:2011:GIG
author: E. J. M. Veling
title: The Generalized Incomplete Gamma Function as sum over Modified Bessel Functions of the First Kind
journal: j-J-COMPUT-APPL-MATH
volume: 235
number: 14
pages: 4107--4116
day: 15
month: may
monthnumber: 5
year: 2011
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 13:24:28 MST 2017
bibtimestamp: 2017.02.25 13:24:28 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042711001245
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: E. J. M. Veling
rawtitle: The Generalized Incomplete Gamma Function as sum over Modified {Bessel} Functions of the First Kind
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2010.bib

entry:
@Article{Veling:2011:GIG,
  author =       "E. J. M. Veling",
  title =        "The Generalized Incomplete Gamma Function as sum over
                 Modified {Bessel} Functions of the First Kind",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "235",
  number =       "14",
  pages =        "4107--4116",
  day =          "15",
  month =        may,
  year =         "2011",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 13:24:28 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2010.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042711001245",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: inproceedings
filename: elefunt.bib
label: Wu:2011:NEL
author: Mingwei Wu and Xuzheng Lin and Pooi-Yuen Kam
booktitle: 2011 IEEE 73rd Vehicular Technology Conference (VTC Spring)
title: New Exponential Lower Bounds on the Gaussian $Q$-Function via Jensen's Inequality
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 4107--4116
month: may
monthnumber: 5
year: 2011
DOI: https://doi.org/10.1109/vetecs.2011.5956392
bibdate: Sat Dec 16 16:53:49 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.12.16 16:53:49 ???
URL: http://ieeexplore.ieee.org/document/5956392/
acknowledgement: ack-nhfb
rawauthor: Mingwei Wu and Xuzheng Lin and Pooi-Yuen Kam
rawbooktitle: {2011 IEEE 73rd Vehicular Technology Conference (VTC Spring)}
rawtitle: New Exponential Lower Bounds on the {Gaussian} {$Q$}-Function via {Jensen}'s Inequality
entry:
@InProceedings{Wu:2011:NEL,
  author =       "Mingwei Wu and Xuzheng Lin and Pooi-Yuen Kam",
  booktitle =    "{2011 IEEE 73rd Vehicular Technology Conference (VTC
                 Spring)}",
  title =        "New Exponential Lower Bounds on the {Gaussian}
                 {$Q$}-Function via {Jensen}'s Inequality",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  month =        may,
  year =         "2011",
  DOI =          "https://doi.org/10.1109/vetecs.2011.5956392",
  bibdate =      "Sat Dec 16 16:53:49 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://ieeexplore.ieee.org/document/5956392/",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Yerukala:2011:ACS
author: R. Yerukala and N. K. Boiroju and M. K. Reddy
title: An Approximation to the CDF of Standard Normal Distribution
journal: International Journal of Mathematical Archive
volume: 2
number: 7
pages: 1077--1079
year: 2011
ISSN: 2229-5046 OR 22295046
ISSNL: 2229-5046 OR 22295046
bibdate: Sat Dec 16 18:03:12 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.12.16 18:03:12 ???
URL: http://ijma.info/index.php/ijma/article/view/393
acknowledgement: ack-nhfb
ajournal: Int. J. Math. Arch.
rawauthor: R. Yerukala and N. K. Boiroju and M. K. Reddy
rawtitle: An Approximation to the {CDF} of Standard Normal Distribution
entry:
@Article{Yerukala:2011:ACS,
  author =       "R. Yerukala and N. K. Boiroju and M. K. Reddy",
  title =        "An Approximation to the {CDF} of Standard Normal
                 Distribution",
  journal =      "International Journal of Mathematical Archive",
  volume =       "2",
  number =       "7",
  pages =        "1077--1079",
  month =        "????",
  year =         "2011",
  ISSN =         "2229-5046",
  ISSN-L =       "2229-5046",
  bibdate =      "Sat Dec 16 18:03:12 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://ijma.info/index.php/ijma/article/view/393",
  acknowledgement = ack-nhfb,
  ajournal =     "Int. J. Math. Arch.",
}


bibtype: article
filename: elefunt.bib
label: Zaghloul:2011:ACF
author: Mofreh R. Zaghloul and Ahmed N. Ali
title: Algorithm 916: Computing the Faddeyeva and Voigt functions
journal: j-TOMS
volume: 38
number: 2
pages: 15:1--15:22
month: dec
monthnumber: 12
year: 2011
CODEN: ACMSCU
DOI: https://doi.org/10.1145/2049673.2049679
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Fri Dec 30 17:43:07 MST 2011
bibtimestamp: 2011.12.30 17:43:07 MST
note: See remark cite Zaghloul:2016:RAC.
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
articleno: 15
journalURL: https://dl.acm.org/loi/toms
rawauthor: Mofreh R. Zaghloul and Ahmed N. Ali
rawnote: See remark \cite{Zaghloul:2016:RAC}.
rawtitle: {Algorithm 916}: Computing the {Faddeyeva} and {Voigt} functions
bibsource:
http://www.acm.org/pubs/contents/journals/toms/; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/matlab.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib

abstract:
We present a MATLAB function for the numerical evaluation of the Faddeyeva function $ w(z) $. The function is based on a newly developed accurate algorithm. In addition to its higher accuracy, the software provides a flexible accuracy vs efficiency trade-off through a controlling parameter that may be used to reduce accuracy and computational time and vice versa. Verification of the flexibility, reliability, and superior accuracy of the algorithm is provided through comparison with standard algorithms available in other libraries and software packages.

rawabstract:
We present a MATLAB function for the numerical evaluation of the Faddeyeva function $ w(z) $. The function is based on a newly developed accurate algorithm. In addition to its higher accuracy, the software provides a flexible accuracy vs efficiency trade-off through a controlling parameter that may be used to reduce accuracy and computational time and vice versa. Verification of the flexibility, reliability, and superior accuracy of the algorithm is provided through comparison with standard algorithms available in other libraries and software packages.

entry:
@Article{Zaghloul:2011:ACF,
  author =       "Mofreh R. Zaghloul and Ahmed N. Ali",
  title =        "{Algorithm 916}: Computing the {Faddeyeva} and {Voigt}
                 functions",
  journal =      j-TOMS,
  volume =       "38",
  number =       "2",
  pages =        "15:1--15:22",
  month =        dec,
  year =         "2011",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2049673.2049679",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Dec 30 17:43:07 MST 2011",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See remark \cite{Zaghloul:2016:RAC}.",
  abstract =     "We present a MATLAB function for the numerical
                 evaluation of the Faddeyeva function $ w(z) $. The
                 function is based on a newly developed accurate
                 algorithm. In addition to its higher accuracy, the
                 software provides a flexible accuracy vs efficiency
                 trade-off through a controlling parameter that may be
                 used to reduce accuracy and computational time and vice
                 versa. Verification of the flexibility, reliability,
                 and superior accuracy of the algorithm is provided
                 through comparison with standard algorithms available
                 in other libraries and software packages.",
  acknowledgement = ack-nhfb,
  articleno =    "15",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: article
filename: elefunt.bib
label: Zhou:2011:ADZ
author: Jian-Rong Zhou and Yu-Qiu Zhao
title: Asymptotic distributions of the zeros of certain classes of Gauss hypergeometric polynomials
journal: j-APPL-MATH-COMP
volume: 218
number: 3
pages: 1153--1159
day: 1
month: oct
monthnumber: 10
year: 2011
CODEN: AMHCBQ
DOI: https://doi.org/10.1016/j.amc.2011.05.106
ISSN: 0096-3003 (print), 1873-5649 (electronic) OR 00963003 (print), 18735649 (electronic)
ISSNL: 0096-3003 OR 00963003
bibdate: Tue Oct 25 09:02:50 MDT 2011
bibtimestamp: 2011.10.25 09:02:50 MDT
note: Special Issue in Honour of Hari M. Srivastava on his 70th birth anniversary.
URL: http://www.sciencedirect.com/science/article/pii/S0096300311007892
fjournal: Applied Mathematics and Computation
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00963003
rawauthor: Jian-Rong Zhou and Yu-Qiu Zhao
rawnote: Special Issue in Honour of Hari M. Srivastava on his 70th birth anniversary.
rawtitle: Asymptotic distributions of the zeros of certain classes of {Gauss} hypergeometric polynomials
bibsource:
http://www.sciencedirect.com/science/journal/00963003; https://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Zhou:2011:ADZ,
  author =       "Jian-Rong Zhou and Yu-Qiu Zhao",
  title =        "Asymptotic distributions of the zeros of certain
                 classes of {Gauss} hypergeometric polynomials",
  journal =      j-APPL-MATH-COMP,
  volume =       "218",
  number =       "3",
  pages =        "1153--1159",
  day =          "1",
  month =        oct,
  year =         "2011",
  CODEN =        "AMHCBQ",
  DOI =          "https://doi.org/10.1016/j.amc.2011.05.106",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Tue Oct 25 09:02:50 MDT 2011",
  bibsource =    "http://www.sciencedirect.com/science/journal/00963003;
                 https://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Special Issue in Honour of Hari M. Srivastava on his
                 70th birth anniversary.",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0096300311007892",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
}


bibtype: article
filename: elefunt.bib
label: Adlaj:2012:EFP
author: Semjon Adlaj
title: An Eloquent Formula for the Perimeter of an Ellipse
journal: j-NAMS
volume: 59
number: 8
pages: 1094--1099
month: sep
monthnumber: 9
year: 2012
CODEN: AMNOAN
ISSN: 0002-9920 (print), 1088-9477 (electronic) OR 00029920 (print), 10889477 (electronic)
ISSNL: 0002-9920 OR 00029920
bibdate: Wed Sep 05 09:12:25 2012
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2012.09.05 09:12:25 ???
URL: http://www.ams.org/notices/201208/rtx120801094p.pdf
fjournal: Notices of the American Mathematical Society
keywords: complete elliptic integral; pendulum; perimeter of ellipse
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/notices/
rawauthor: Semjon Adlaj
rawtitle: An Eloquent Formula for the Perimeter of an Ellipse
remark:
This paper introduces several arithmetic-geometric mean (AGM) algorithms for fast and practical computation of complete elliptic integrals.

entry:
@Article{Adlaj:2012:EFP,
  author =       "Semjon Adlaj",
  title =        "An Eloquent Formula for the Perimeter of an Ellipse",
  journal =      j-NAMS,
  volume =       "59",
  number =       "8",
  pages =        "1094--1099",
  month =        sep,
  year =         "2012",
  CODEN =        "AMNOAN",
  ISSN =         "0002-9920 (print), 1088-9477 (electronic)",
  ISSN-L =       "0002-9920",
  bibdate =      "Wed Sep 05 09:12:25 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.ams.org/notices/201208/rtx120801094p.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Notices of the American Mathematical Society",
  journal-URL =  "http://www.ams.org/notices/",
  keywords =     "complete elliptic integral; pendulum; perimeter of
                 ellipse",
  remark =       "This paper introduces several arithmetic-geometric
                 mean (AGM) algorithms for fast and practical
                 computation of complete elliptic integrals.",
}


bibtype: article
filename: elefunt.bib
label: Al-Mohy:2012:MAB
author: Awad H. Al-Mohy
title: A more accurate Briggs method for the logarithm
journal: j-NUMER-ALGORITHMS
volume: 59
number: 3
pages: 393--402
month: mar
monthnumber: 3
year: 2012
CODEN: NUALEG
DOI: https://doi.org/10.1007/s11075-011-9496-z
ISSN: 1017-1398 (print), 1572-9265 (electronic) OR 10171398 (print), 15729265 (electronic)
ISSNL: 1017-1398 OR 10171398
bibdate: Fri Oct 26 08:07:24 MDT 2012
bibtimestamp: 2012.10.26 08:07:24 MDT
fjournal: Numerical Algorithms
keywords: Briggs' method; Briggs' tables; Inverse scaling and squaring method; Logarithm function
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/11075
rawauthor: Awad H. Al-Mohy
rawtitle: A more accurate {Briggs} method for the logarithm
bibsource:
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1017-1398&volume=59&issue=3; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib

URL:
http://www.springerlink.com/content/4110609h521kg66m/; http://www.springerlink.com/openurl.asp?genre=article&issn=1017-1398&volume=59&issue=3&spage=393

abstract:
A new approach for computing an expression of the form $ a^1 / 2^k - 1 $ is presented that avoids the danger of subtractive cancellation in floating point arithmetic, where $a$ is a complex number not belonging to the closed negative real axis and $k$ is a nonnegative integer. We also derive a condition number for the problem. The algorithm therefore allows highly accurate numerical calculation of $ log (a) $ using Briggs' method.

rawabstract:
A new approach for computing an expression of the form $ a^{1 / 2^k} - 1 $ is presented that avoids the danger of subtractive cancellation in floating point arithmetic, where $a$ is a complex number not belonging to the closed negative real axis and $k$ is a nonnegative integer. We also derive a condition number for the problem. The algorithm therefore allows highly accurate numerical calculation of $ \log (a) $ using Briggs' method.

entry:
@Article{Al-Mohy:2012:MAB,
  author =       "Awad H. Al-Mohy",
  title =        "A more accurate {Briggs} method for the logarithm",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "59",
  number =       "3",
  pages =        "393--402",
  month =        mar,
  year =         "2012",
  CODEN =        "NUALEG",
  DOI =          "https://doi.org/10.1007/s11075-011-9496-z",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Fri Oct 26 08:07:24 MDT 2012",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1017-1398&volume=59&issue=3;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
  URL =          "http://www.springerlink.com/content/4110609h521kg66m/;
                 http://www.springerlink.com/openurl.asp?genre=article&issn=1017-1398&volume=59&issue=3&spage=393",
  abstract =     "A new approach for computing an expression of the form
                 $ a^{1 / 2^k} - 1 $ is presented that avoids the danger
                 of subtractive cancellation in floating point
                 arithmetic, where $a$ is a complex number not belonging
                 to the closed negative real axis and $k$ is a
                 nonnegative integer. We also derive a condition number
                 for the problem. The algorithm therefore allows highly
                 accurate numerical calculation of $ \log (a) $ using
                 Briggs' method.",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
  keywords =     "Briggs' method; Briggs' tables; Inverse scaling and
                 squaring method; Logarithm function",
}


bibtype: misc
filename: elefunt.bib
label: Anonymous:2012:FIS
author: Anonymous
title: Fast inverse square root
pages: 393--402
day: 20
month: mar
monthnumber: 3
year: 2012
bibdate: Mon Apr 02 17:03:18 2012
bibtimestamp: 2012.04.02 17:03:18 ???
URL: http://en.wikipedia.org/wiki/Fast_inverse_square_root
acknowledgement: ack-nhfb
howpublished: Wikipedia article.
rawauthor: Anonymous
rawtitle: Fast inverse square root
note:
This article describes an algorithm for the inverse square root. The only novel feature is use of two IEEE-754 specific magic constants for 32-bit and 64-bit binary arithmetic that allow obtaining fast starting estimates for Newton--Raphson iterations by manipulating the floating-point representations as integers. The code fails to handle signed zero, Infinity, and NaN arguments, uses too few iterations, and does not adjust for rounding errors to obtain correctly-rounded results. See cite Blinn:1997:JBC.

rawnote:
This article describes an algorithm for the inverse square root. The only novel feature is use of two IEEE-754 specific magic constants for 32-bit and 64-bit binary arithmetic that allow obtaining fast starting estimates for Newton--Raphson iterations by manipulating the floating-point representations as integers. The code fails to handle signed zero, Infinity, and NaN arguments, uses too few iterations, and does not adjust for rounding errors to obtain correctly-rounded results. See \cite{Blinn:1997:JBC}.

entry:
@Misc{Anonymous:2012:FIS,
  author =       "Anonymous",
  title =        "Fast inverse square root",
  howpublished = "Wikipedia article.",
  day =          "20",
  month =        mar,
  year =         "2012",
  bibdate =      "Mon Apr 02 17:03:18 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "This article describes an algorithm for the inverse
                 square root. The only novel feature is use of two
                 IEEE-754 specific magic constants for 32-bit and 64-bit
                 binary arithmetic that allow obtaining fast starting
                 estimates for Newton--Raphson iterations by
                 manipulating the floating-point representations as
                 integers. The code fails to handle signed zero,
                 Infinity, and NaN arguments, uses too few iterations,
                 and does not adjust for rounding errors to obtain
                 correctly-rounded results. See \cite{Blinn:1997:JBC}.",
  URL =          "http://en.wikipedia.org/wiki/Fast_inverse_square_root",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Bailey:2012:AIS
author: David H. Bailey and Jonathan M. Borwein
title: Ancient Indian Square Roots: An Exercise in Forensic Paleo-Mathematics
journal: j-AMER-MATH-MONTHLY
volume: 119
number: 8
pages: 646--657
month: oct
monthnumber: 10
year: 2012
CODEN: AMMYAE
DOI: https://doi.org/10.4169/amer.math.monthly.119.08.646
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
bibdate: Thu Nov 8 07:34:21 MST 2012
bibtimestamp: 2012.11.08 07:34:21 MST
URL: http://www.jstor.org/stable/pdfplus/10.4169/amer.math.monthly.119.08.646.pdf
fjournal: American Mathematical Monthly
acknowledgement: ack-nhfb
journalURL: https://www.jstor.org/journals/00029890.htm
rawauthor: David H. Bailey and Jonathan M. Borwein
rawtitle: Ancient {Indian} Square Roots: An Exercise in Forensic Paleo-Mathematics
bibsource:
http://www.jstor.org/journals/00029890.html; http://www.jstor.org/stable/10.4169/amermathmont.119.issue-8; https://www.math.utah.edu/pub/tex/bib/amermathmonthly2010.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Bailey:2012:AIS,
  author =       "David H. Bailey and Jonathan M. Borwein",
  title =        "Ancient {Indian} Square Roots: An Exercise in Forensic
                 Paleo-Mathematics",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "119",
  number =       "8",
  pages =        "646--657",
  month =        oct,
  year =         "2012",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.4169/amer.math.monthly.119.08.646",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Thu Nov 8 07:34:21 MST 2012",
  bibsource =    "http://www.jstor.org/journals/00029890.html;
                 http://www.jstor.org/stable/10.4169/amermathmont.119.issue-8;
                 https://www.math.utah.edu/pub/tex/bib/amermathmonthly2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.jstor.org/stable/pdfplus/10.4169/amer.math.monthly.119.08.646.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
}


bibtype: inproceedings
filename: elefunt.bib
label: Brisebarre:2012:MPK
author: Nicolas Brisebarre and Milo D. Ercegovac and Jean-Michel Muller
editor: IEEE
title: $ (M, p, k) $-Friendly Points: a Table-Based Method for Trigonometric Function Evaluation
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 46--52
year: 2012
DOI: https://doi.org/10.1109/ASAP.2012.17
ISBN: 0-7695-4768-0 OR 0769547680
ISBN13: 978-0-7695-4768-8 OR 9780769547688
ISSN: 1063-6862 OR 10636862
ISSNL: 1063-6862 OR 10636862
bibdate: Fri Sep 29 10:49:22 2023
bibtimestamp: 2023.09.29 10:49:22 ???
acknowledgement: ack-nhfb
rawauthor: Nicolas Brisebarre and Milo D. Ercegovac and Jean-Michel Muller
raweditor: {IEEE}
rawtitle: {$ (M, p, k) $}-Friendly Points: a Table-Based Method for Trigonometric Function Evaluation
booktitle:
2012 IEEE 23rd International Conference on Application-Specific Systems, Architectures and Processors, 9--11 July 2012. Delft, The Netherlands

rawbooktitle:
{2012 IEEE 23rd International Conference on Application-Specific Systems, Architectures and Processors, 9--11 July 2012. Delft, The Netherlands}

entry:
@InProceedings{Brisebarre:2012:MPK,
  author =       "Nicolas Brisebarre and Milo D. Ercegovac and
                 Jean-Michel Muller",
  editor =       "{IEEE}",
  booktitle =    "{2012 IEEE 23rd International Conference on
                 Application-Specific Systems, Architectures and
                 Processors, 9--11 July 2012. Delft, The Netherlands}",
  title =        "{$ (M, p, k) $}-Friendly Points: a Table-Based Method
                 for Trigonometric Function Evaluation",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "46--52",
  year =         "2012",
  DOI =          "https://doi.org/10.1109/ASAP.2012.17",
  ISBN =         "0-7695-4768-0",
  ISBN-13 =      "978-0-7695-4768-8",
  ISSN =         "1063-6862",
  ISSN-L =       "1063-6862",
  bibdate =      "Fri Sep 29 10:49:22 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Chen:2012:SIM
author: Chao-Ping Chen and Necdet Batir
title: Some inequalities and monotonicity properties associated with the gamma and psi functions
journal: j-APPL-MATH-COMP
volume: 218
number: 17
pages: 8217--8225
day: 1
month: may
monthnumber: 5
year: 2012
CODEN: AMHCBQ
DOI: https://doi.org/10.1016/j.amc.2012.02.007
ISSN: 0096-3003 (print), 1873-5649 (electronic) OR 00963003 (print), 18735649 (electronic)
ISSNL: 0096-3003 OR 00963003
bibdate: Thu Apr 5 06:00:26 MDT 2012
bibtimestamp: 2012.04.05 06:00:26 MDT
URL: http://www.sciencedirect.com/science/article/pii/S0096300312001257
fjournal: Applied Mathematics and Computation
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00963003
rawauthor: Chao-Ping Chen and Necdet Batir
rawtitle: Some inequalities and monotonicity properties associated with the gamma and psi functions
bibsource:
http://www.sciencedirect.com/science/journal/00963003; https://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

remark:
New bounds on the gamma function in terms of the psi function, and a new estimate for the error in Stirling's formula, $ Gamma (x + 1) approx x^x e^-x sqrt 2 pi x $.

entry:
@Article{Chen:2012:SIM,
  author =       "Chao-Ping Chen and Necdet Batir",
  title =        "Some inequalities and monotonicity properties
                 associated with the gamma and psi functions",
  journal =      j-APPL-MATH-COMP,
  volume =       "218",
  number =       "17",
  pages =        "8217--8225",
  day =          "1",
  month =        may,
  year =         "2012",
  CODEN =        "AMHCBQ",
  DOI =          "https://doi.org/10.1016/j.amc.2012.02.007",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Thu Apr 5 06:00:26 MDT 2012",
  bibsource =    "http://www.sciencedirect.com/science/journal/00963003;
                 https://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0096300312001257",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
  remark =       "New bounds on the gamma function in terms of the psi
                 function, and a new estimate for the error in
                 Stirling's formula, $ \Gamma (x + 1) \approx x^x e^{-x}
                 \sqrt {2 \pi x} $.",
}


bibtype: article
filename: elefunt.bib
label: Cohl:2012:TEF
author: Howard S. Cohl
journal: j-MATH-COMPUT
volume: 81
number: 280
pages: 2251--2251
month: oct
monthnumber: 10
year: 2012
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Nov 6 09:52:53 MST 2012
bibtimestamp: 2012.11.06 09:52:53 MST
note: See cite Magnus:1966:FTS.
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Howard S. Cohl
rawnote: See \cite{Magnus:1966:FTS}.
title:
Table Errata to ``Formulas and theorems for the special functions of mathematical physics'' by W. Magnus, F. Oberhettinger & R. P. Soni (1966)

bibsource:
http://www.ams.org/mcom/2012-81-280; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp2010.bib

URL:
http://www.ams.org/journals/mcom/2012-81-280/S0025-5718-2012-02612-3; http://www.ams.org/journals/mcom/2012-81-280/S0025-5718-2012-02612-3/S0025-5718-2012-02612-3.pdf

remark:
Report of sign error in a sum of two Gauss hypergeometric functions for Ferrers function of the second kind.

rawtitle:
Table Errata to {``Formulas and theorems for the special functions of mathematical physics'' by W. Magnus, F. Oberhettinger \& R. P. Soni (1966)}

entry:
@Article{Cohl:2012:TEF,
  author =       "Howard S. Cohl",
  title =        "Table Errata to {``Formulas and theorems for the
                 special functions of mathematical physics'' by W.
                 Magnus, F. Oberhettinger \& R. P. Soni (1966)}",
  journal =      j-MATH-COMPUT,
  volume =       "81",
  number =       "280",
  pages =        "2251--2251",
  month =        oct,
  year =         "2012",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Nov 6 09:52:53 MST 2012",
  bibsource =    "http://www.ams.org/mcom/2012-81-280;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp2010.bib",
  note =         "See \cite{Magnus:1966:FTS}.",
  URL =          "http://www.ams.org/journals/mcom/2012-81-280/S0025-5718-2012-02612-3;
                 http://www.ams.org/journals/mcom/2012-81-280/S0025-5718-2012-02612-3/S0025-5718-2012-02612-3.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  remark =       "Report of sign error in a sum of two Gauss
                 hypergeometric functions for Ferrers function of the
                 second kind.",
}


bibtype: article
filename: elefunt.bib
label: Cote:2012:CTL
author: F. D. Cote and I. N. Psaromiligkos and W. J. Gross
title: A Chernoff-type lower bound for the Gaussian $Q$-function
journal: arxiv.org
pages: ??--??
year: 2012
bibdate: Sat Dec 16 16:04:00 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.12.16 16:04:00 ???
URL: https://arxiv.org/abs/1202.6483
acknowledgement: ack-nhfb
rawauthor: F. D. C{\^o}t{\'e} and I. N. Psaromiligkos and W. J. Gross
rawtitle: A {Chernoff}-type lower bound for the {Gaussian} {$Q$}-function
entry:
@Article{Cote:2012:CTL,
  author =       "F. D. C{\^o}t{\'e} and I. N. Psaromiligkos and W. J.
                 Gross",
  title =        "A {Chernoff}-type lower bound for the {Gaussian}
                 {$Q$}-function",
  journal =      "arxiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  year =         "2012",
  bibdate =      "Sat Dec 16 16:04:00 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://arxiv.org/abs/1202.6483",
  acknowledgement = ack-nhfb,
  pagecount =    "3",
}


bibtype: book
filename: elefunt.bib
label: Crandall:2012:ARS
author: Richard E. Crandall
title: Algorithmic Reflections: Selected Works
publisher: PSI Press
address: Portland, OR, USA
edition: First Perfectly Scientific Press paperback
pages: 410
year: 2012
ISBN: 1-935638-19-X OR 193563819X
ISBN13: 978-1-935638-19-3 OR 9781935638193
LCCN: QA958 .C736 2012
bibdate: Fri Jun 30 11:14:26 MDT 2023
bibtimestamp: 2023.06.30 11:14:26 MDT
subject: Algorithms; Algorithmes
acknowledgement: ack-nhfb
authordates: 1947--2012
rawauthor: Richard E. Crandall
rawtitle: Algorithmic Reflections: Selected Works
bibsource:
fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

TOC:
Part I: Number theory On the $ 3 x + 1$ problem On a conjecture of Crandall concerning the $ q n + 1$ problem A search for Wieferich and Wilson primes Parallelization of Pollard-rho factorization Three new factors of Fermat numbers Random generators and normal numbers The googol-th bit of the Erdos--Borwein constant Part II: Analytical algorithms Fast evaluation of multiple zeta sums On the Khintchine Constant On the dynamics of certain recurrence relations Effective Laguerre asymptotics Theory of ROOF walks Unified algorithms for polylogarithm, $L$-series, and zeta variants Part III: Physics, biology, epidemics, and physiology The potential within a crystal lattice The fractal character of space-time epidemics Mathematical signatures as tools for visual dysfunction NLA system for medical-data classification On the fractal distribution of brain synapses

rawTOC:
Part I: Number theory \\ On the $ 3 x + 1$ problem \\ On a conjecture of Crandall concerning the $ q n + 1$ problem \\ A search for Wieferich and Wilson primes \\ Parallelization of Pollard-rho factorization \\ Three new factors of Fermat numbers \\ Random generators and normal numbers \\ The googol-th bit of the Erd{\H{o}}s--Borwein constant \\ Part II: Analytical algorithms \\ Fast evaluation of multiple zeta sums \\ On the Khintchine Constant \\ On the dynamics of certain recurrence relations \\ Effective Laguerre asymptotics \\ Theory of ROOF walks \\ Unified algorithms for polylogarithm, $L$-series, and zeta variants \\ Part III: Physics, biology, epidemics, and physiology \\ The potential within a crystal lattice \\ The fractal character of space-time epidemics \\ Mathematical signatures as tools for visual dysfunction \\ NLA system for medical-data classification \\ On the fractal distribution of brain synapses

entry:
@Book{Crandall:2012:ARS,
  author =       "Richard E. Crandall",
  title =        "Algorithmic Reflections: Selected Works",
  publisher =    "PSI Press",
  address =      "Portland, OR, USA",
  edition =      "First Perfectly Scientific Press paperback",
  pages =        "410",
  year =         "2012",
  ISBN =         "1-935638-19-X",
  ISBN-13 =      "978-1-935638-19-3",
  LCCN =         "QA958 .C736 2012",
  bibdate =      "Fri Jun 30 11:14:26 MDT 2023",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  author-dates = "1947--2012",
  subject =      "Algorithms; Algorithmes",
  tableofcontents = "Part I: Number theory \\
                 On the $ 3 x + 1$ problem \\
                 On a conjecture of Crandall concerning the $ q n + 1$
                 problem \\
                 A search for Wieferich and Wilson primes \\
                 Parallelization of Pollard-rho factorization \\
                 Three new factors of Fermat numbers \\
                 Random generators and normal numbers \\
                 The googol-th bit of the Erd{\H{o}}s--Borwein constant
                 \\
                 Part II: Analytical algorithms \\
                 Fast evaluation of multiple zeta sums \\
                 On the Khintchine Constant \\
                 On the dynamics of certain recurrence relations \\
                 Effective Laguerre asymptotics \\
                 Theory of ROOF walks \\
                 Unified algorithms for polylogarithm, $L$-series, and
                 zeta variants \\
                 Part III: Physics, biology, epidemics, and physiology
                 \\
                 The potential within a crystal lattice \\
                 The fractal character of space-time epidemics \\
                 Mathematical signatures as tools for visual dysfunction
                 \\
                 NLA system for medical-data classification \\
                 On the fractal distribution of brain synapses",
}


bibtype: misc
filename: elefunt.bib
label: Crandall:2012:UAP
author: R. E. Crandall
title: Unified algorithms for polylogarithm, $L$-series, and zeta variants
type: Preprint
pages: 53
year: 2012
bibdate: Tue Sep 09 11:50:04 2014
bibtimestamp: 2014.09.09 11:50:04 ???
note: Published in cite Crandall:2012:ARS.
acknowledgement: ack-nhfb
rawauthor: R. E. Crandall
rawnote: Published in \cite{Crandall:2012:ARS}.
rawtitle: Unified algorithms for polylogarithm, {$L$}-series, and zeta variants
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

URL:
http://www.perfscipress.com/papers/universalTOC25.pdf; https://web.archive.org/web/20130430193005/http://www.perfscipress.com/papers/universalTOC25.pdf

abstract:
We describe a general computational scheme for evaluation of a wide class of number-theoretical functions. We avoid asymptotic expansions in favor of manifestly convergent series that lend themselves naturally to rigorous error bounds. By employing three fundamental series algorithms we achieve a unified strategy to compute the various functions via parameter selection. This work amounts to a compendium of methods to establish extreme-precision results as typify modern experimental mathematics. A fortuitous byproduct of this unified approach is automatic analytic continuation over complex parameters. Another byproduct is a host of converging series for various fundamental constants.

rawabstract:
We describe a general computational scheme for evaluation of a wide class of number-theoretical functions. We avoid asymptotic expansions in favor of manifestly convergent series that lend themselves naturally to rigorous error bounds. By employing three fundamental series algorithms we achieve a unified strategy to compute the various functions via parameter selection. This work amounts to a compendium of methods to establish extreme-precision results as typify modern experimental mathematics. A fortuitous byproduct of this unified approach is automatic analytic continuation over complex parameters. Another byproduct is a host of converging series for various fundamental constants.

entry:
@Misc{Crandall:2012:UAP,
  author =       "R. E. Crandall",
  title =        "Unified algorithms for polylogarithm, {$L$}-series,
                 and zeta variants",
  type =         "Preprint",
  pages =        "53",
  year =         "2012",
  bibdate =      "Tue Sep 09 11:50:04 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Published in \cite{Crandall:2012:ARS}.",
  URL =          "http://www.perfscipress.com/papers/universalTOC25.pdf;
                 https://web.archive.org/web/20130430193005/http://www.perfscipress.com/papers/universalTOC25.pdf",
  abstract =     "We describe a general computational scheme for
                 evaluation of a wide class of number-theoretical
                 functions. We avoid asymptotic expansions in favor of
                 manifestly convergent series that lend themselves
                 naturally to rigorous error bounds. By employing three
                 fundamental series algorithms we achieve a unified
                 strategy to compute the various functions via parameter
                 selection. This work amounts to a compendium of methods
                 to establish extreme-precision results as typify modern
                 experimental mathematics. A fortuitous byproduct of
                 this unified approach is automatic analytic
                 continuation over complex parameters. Another byproduct
                 is a host of converging series for various fundamental
                 constants.",
  acknowledgement = ack-nhfb,
  remark-1 =     "In memory of gentle colleague Jerry Keiper
                 (1953--1995).",
  remark-2 =     "Host in URL field no longer exists; cited in
                 \cite{Coffey:2014:SRR}.",
}


bibtype: article
filename: elefunt.bib
label: DeSchrijver:2012:DPRa
author: Steven K. De Schrijver and El-Houssaine Aghezzaf and Hendrik Vanmaele
journal: j-APPL-MATH-COMP
volume: 219
number: 3
pages: 1375--1382
day: 15
month: oct
monthnumber: 10
year: 2012
CODEN: AMHCBQ
DOI: https://doi.org/10.1016/j.amc.2012.07.011
ISSN: 0096-3003 (print), 1873-5649 (electronic) OR 00963003 (print), 18735649 (electronic)
ISSNL: 0096-3003 OR 00963003
bibdate: Thu Oct 25 09:05:16 MDT 2012
bibtimestamp: 2012.10.25 09:05:16 MDT
URL: http://www.sciencedirect.com/science/article/pii/S0096300312007114
fjournal: Applied Mathematics and Computation
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00963003
rawauthor: Steven K. {De Schrijver} and El-Houssaine Aghezzaf and Hendrik Vanmaele
title:
Double precision rational approximation algorithm for the inverse standard normal first order loss function

rawtitle:
Double precision rational approximation algorithm for the inverse standard normal first order loss function

entry:
@Article{DeSchrijver:2012:DPRa,
  author =       "Steven K. {De Schrijver} and El-Houssaine Aghezzaf and
                 Hendrik Vanmaele",
  title =        "Double precision rational approximation algorithm for
                 the inverse standard normal first order loss function",
  journal =      j-APPL-MATH-COMP,
  volume =       "219",
  number =       "3",
  pages =        "1375--1382",
  day =          "15",
  month =        oct,
  year =         "2012",
  CODEN =        "AMHCBQ",
  DOI =          "https://doi.org/10.1016/j.amc.2012.07.011",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Thu Oct 25 09:05:16 MDT 2012",
  bibsource =    "http://www.sciencedirect.com/science/journal/00963003;
                 https://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0096300312007114",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
}


bibtype: article
filename: elefunt.bib
label: DeSchrijver:2012:DPRb
author: Steven K. De Schrijver and El-Houssaine Aghezzaf and Hendrik Vanmaele
journal: j-APPL-MATH-COMP
volume: 219
number: 4
pages: 2320--2330
day: 1
month: nov
monthnumber: 11
year: 2012
CODEN: AMHCBQ
DOI: https://doi.org/10.1016/j.amc.2012.08.012
ISSN: 0096-3003 (print), 1873-5649 (electronic) OR 00963003 (print), 18735649 (electronic)
ISSNL: 0096-3003 OR 00963003
bibdate: Thu Oct 25 09:05:21 MDT 2012
bibtimestamp: 2012.10.25 09:05:21 MDT
URL: http://www.sciencedirect.com/science/article/pii/S0096300312008041
fjournal: Applied Mathematics and Computation
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00963003
rawauthor: Steven K. {De Schrijver} and El-Houssaine Aghezzaf and Hendrik Vanmaele
title:
Double precision rational approximation algorithms for the standard normal first and second order loss functions

rawtitle:
Double precision rational approximation algorithms for the standard normal first and second order loss functions

entry:
@Article{DeSchrijver:2012:DPRb,
  author =       "Steven K. {De Schrijver} and El-Houssaine Aghezzaf and
                 Hendrik Vanmaele",
  title =        "Double precision rational approximation algorithms for
                 the standard normal first and second order loss
                 functions",
  journal =      j-APPL-MATH-COMP,
  volume =       "219",
  number =       "4",
  pages =        "2320--2330",
  day =          "1",
  month =        nov,
  year =         "2012",
  CODEN =        "AMHCBQ",
  DOI =          "https://doi.org/10.1016/j.amc.2012.08.012",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Thu Oct 25 09:05:21 MDT 2012",
  bibsource =    "http://www.sciencedirect.com/science/journal/00963003;
                 https://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0096300312008041",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
}


bibtype: article
filename: elefunt.bib
label: Develi:2012:NAB
author: I. Develi
title: A new approximation based on the differential evolution algorithm for the Gaussian $Q$-function
journal: Int. J. Innov. Comput. Inf. Control
volume: 8
number: 10(B)
pages: 7095--7102
year: 2012
bibdate: Sat Dec 16 16:14:27 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.12.16 16:14:27 ???
acknowledgement: ack-nhfb
rawauthor: I. Develi
rawtitle: A new approximation based on the differential evolution algorithm for the {Gaussian} {$Q$}-function
URL:
http://link.springer.com/content/pdf/10.1007/s10957-012-0217-0.pdf; http://www.ijicic.org/ijicic-11-08039.pdf

entry:
@Article{Develi:2012:NAB,
  author =       "I. Develi",
  title =        "A new approximation based on the differential
                 evolution algorithm for the {Gaussian} {$Q$}-function",
  journal =      "Int. J. Innov. Comput. Inf. Control",
  volume =       "8",
  number =       "10(B)",
  pages =        "7095--7102",
  month =        "????",
  year =         "2012",
  bibdate =      "Sat Dec 16 16:14:27 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://link.springer.com/content/pdf/10.1007/s10957-012-0217-0.pdf;
                 http://www.ijicic.org/ijicic-11-08039.pdf",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Fukushima:2012:SES
author: Toshio Fukushima
title: Series expansions of symmetric elliptic integrals
journal: j-MATH-COMPUT
volume: 81
number: 278
pages: 957--990
year: 2012
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Sat Feb 4 09:28:39 MST 2012
bibtimestamp: 2012.02.04 09:28:39 MST
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Toshio Fukushima
rawtitle: Series expansions of symmetric elliptic integrals
bibsource:
http://www.ams.org/mcom/2012-81-278; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp2010.bib

URL:
http://www.ams.org/journals/mcom/2012-81-278/S0025-5718-2011-02531-7; http://www.ams.org/journals/mcom/2012-81-278/S0025-5718-2011-02531-7/S0025-5718-2011-02531-7.pdf

abstract:
Based on general discussion of series expansions of Carlson's symmetric elliptic integrals, we developed fifteen kinds of them including eleven new ones by utilizing the symmetric nature of the integrals. Thanks to the special addition formulas of the integrals, we also obtained their complementary series expansions. By considering the balance between the speed of convergence and the amount of computational labor, we chose four of them as the best series expansions. Practical evaluation of the integrals is conducted by the most suitable one among these four series expansions. Its selection rule was analytically specified in terms of the numerical values of given parameters. As a by-product, we obtained an efficient asymptotic expansion of the integrals around their logarithmic singularities. Numerical experiments confirmed the effectiveness of these new series expansions.

rawabstract:
Based on general discussion of series expansions of Carlson's symmetric elliptic integrals, we developed fifteen kinds of them including eleven new ones by utilizing the symmetric nature of the integrals. Thanks to the special addition formulas of the integrals, we also obtained their complementary series expansions. By considering the balance between the speed of convergence and the amount of computational labor, we chose four of them as the best series expansions. Practical evaluation of the integrals is conducted by the most suitable one among these four series expansions. Its selection rule was analytically specified in terms of the numerical values of given parameters. As a by-product, we obtained an efficient asymptotic expansion of the integrals around their logarithmic singularities. Numerical experiments confirmed the effectiveness of these new series expansions.

entry:
@Article{Fukushima:2012:SES,
  author =       "Toshio Fukushima",
  title =        "Series expansions of symmetric elliptic integrals",
  journal =      j-MATH-COMPUT,
  volume =       "81",
  number =       "278",
  pages =        "957--990",
  month =        "",
  year =         "2012",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Sat Feb 4 09:28:39 MST 2012",
  bibsource =    "http://www.ams.org/mcom/2012-81-278;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp2010.bib",
  URL =          "http://www.ams.org/journals/mcom/2012-81-278/S0025-5718-2011-02531-7;
                 http://www.ams.org/journals/mcom/2012-81-278/S0025-5718-2011-02531-7/S0025-5718-2011-02531-7.pdf",
  abstract =     "Based on general discussion of series expansions of
                 Carlson's symmetric elliptic integrals, we developed
                 fifteen kinds of them including eleven new ones by
                 utilizing the symmetric nature of the integrals. Thanks
                 to the special addition formulas of the integrals, we
                 also obtained their complementary series expansions. By
                 considering the balance between the speed of
                 convergence and the amount of computational labor, we
                 chose four of them as the best series expansions.
                 Practical evaluation of the integrals is conducted by
                 the most suitable one among these four series
                 expansions. Its selection rule was analytically
                 specified in terms of the numerical values of given
                 parameters. As a by-product, we obtained an efficient
                 asymptotic expansion of the integrals around their
                 logarithmic singularities. Numerical experiments
                 confirmed the effectiveness of these new series
                 expansions.",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Gaudreau:2012:CTP
author: Philippe Gaudreau and Richard M. Slevinsky and Hassan Safouhi
journal: j-SIAM-J-SCI-COMP
volume: 34
number: 1
pages: B65--B85
month: jan
monthnumber: 1
year: 2012
CODEN: SJOCE3
DOI: https://doi.org/10.1137/100803778
ISSN: 1064-8275 (print), 1095-7197 (electronic) OR 10648275 (print), 10957197 (electronic)
ISSNL: 1064-8275 OR 10648275
bibdate: Sat Dec 16 16:33:00 2017
bibtimestamp: 2017.12.16 16:33:00 ???
URL: http://epubs.siam.org/doi/abs/10.1137/100803778
fjournal: SIAM Journal on Scientific Computing
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sisc
rawauthor: Philippe Gaudreau and Richard M. Slevinsky and Hassan Safouhi
title:
Computation of Tail Probabilities via Extrapolation Methods and Connection with Rational and Pade Approximants

bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib

rawtitle:
Computation of Tail Probabilities via Extrapolation Methods and Connection with Rational and {Pad{\'e}} Approximants

entry:
@Article{Gaudreau:2012:CTP,
  author =       "Philippe Gaudreau and Richard M. Slevinsky and Hassan
                 Safouhi",
  title =        "Computation of Tail Probabilities via Extrapolation
                 Methods and Connection with Rational and {Pad{\'e}}
                 Approximants",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "34",
  number =       "1",
  pages =        "B65--B85",
  month =        jan,
  year =         "2012",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/100803778",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  bibdate =      "Sat Dec 16 16:33:00 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
  URL =          "http://epubs.siam.org/doi/abs/10.1137/100803778",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
}


bibtype: article
filename: elefunt.bib
label: Gil:2012:CRZ
author: Amparo Gil and Javier Segura
journal: j-COMPUT-MATH-APPL
volume: 64
number: 1
pages: 11--21
month: jul
monthnumber: 7
year: 2012
CODEN: CMAPDK
DOI: https://doi.org/10.1016/j.camwa.2012.02.032
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Wed Mar 1 21:51:09 MST 2017
bibtimestamp: 2017.03.01 21:51:09 MST
URL: http://www.sciencedirect.com/science/article/pii/S0898122112001460
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/08981221
rawauthor: Amparo Gil and Javier Segura
title:
Computing the real zeros of cylinder functions and the roots of the equation $ x C^prime _nu (x) + gamma C_nu (x) = 0 $

remark:
From the abstract: ``Fast methods to compute the zeros of general cylinder functions $ C_nu (x) = cos alpha J_nu (x) - sin alpha Y_nu (x) C_nu (x) = cos alpha J_nu (x) - sin alpha Y_nu (x) $ in real intervals can be obtained from an approximate integration of the second order ODE satisfied by these functions, leading to fourth order methods with global convergence.''

rawtitle:
Computing the real zeros of cylinder functions and the roots of the equation {$ x C^\prime_\nu (x) + \gamma C_\nu (x) = 0 $}

entry:
@Article{Gil:2012:CRZ,
  author =       "Amparo Gil and Javier Segura",
  title =        "Computing the real zeros of cylinder functions and the
                 roots of the equation {$ x C^\prime_\nu (x) + \gamma
                 C_\nu (x) = 0 $}",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "64",
  number =       "1",
  pages =        "11--21",
  month =        jul,
  year =         "2012",
  CODEN =        "CMAPDK",
  DOI =          "https://doi.org/10.1016/j.camwa.2012.02.032",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 21:51:09 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0898122112001460",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
  remark =       "From the abstract: ``Fast methods to compute the zeros
                 of general cylinder functions $ C_\nu (x) = \cos \alpha
                 J_\nu (x) - \sin \alpha Y_\nu (x) C_\nu (x) = \cos
                 \alpha J_\nu (x) - \sin \alpha Y_\nu (x) $ in real
                 intervals can be obtained from an approximate
                 integration of the second order ODE satisfied by these
                 functions, leading to fourth order methods with global
                 convergence.''",
}


bibtype: article
filename: elefunt.bib
label: Gil:2012:EAA
author: Amparo Gil and Javier Segura and Nico M. Temme
journal: j-SIAM-J-SCI-COMP
volume: 34
number: 6
pages: A2965--A2981
year: 2012
CODEN: SJOCE3
DOI: https://doi.org/10.1137/120872553
ISSN: 1064-8275 (print), 1095-7197 (electronic) OR 10648275 (print), 10957197 (electronic)
ISSNL: 1064-8275 OR 10648275
bibdate: Fri Jul 19 07:43:33 MDT 2013
bibtimestamp: 2013.07.19 07:43:33 MDT
fjournal: SIAM Journal on Scientific Computing
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sisc
onlinedate: January 2012
rawauthor: Amparo Gil and Javier Segura and Nico M. Temme
title:
Efficient and Accurate Algorithms for the Computation and Inversion of the Incomplete Gamma Function Ratios

bibsource:
http://epubs.siam.org/sam-bin/dbq/toc/SISC/34/6; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib

rawtitle:
Efficient and Accurate Algorithms for the Computation and Inversion of the Incomplete Gamma Function Ratios

entry:
@Article{Gil:2012:EAA,
  author =       "Amparo Gil and Javier Segura and Nico M. Temme",
  title =        "Efficient and Accurate Algorithms for the Computation
                 and Inversion of the Incomplete Gamma Function Ratios",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "34",
  number =       "6",
  pages =        "A2965--A2981",
  month =        "????",
  year =         "2012",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/120872553",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  bibdate =      "Fri Jul 19 07:43:33 MDT 2013",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SISC/34/6;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
  onlinedate =   "January 2012",
}


bibtype: article
filename: elefunt.bib
label: Gil:2012:IAF
author: Amparo Gil and Javier Segura and Nico M. Temme
journal: j-COMP-PHYS-COMM
volume: 183
number: 3
pages: 794--799
month: mar
monthnumber: 3
year: 2012
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/j.cpc.2011.11.025
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Sat Feb 11 10:11:02 MST 2012
bibtimestamp: 2012.02.11 10:11:02 MST
URL: http://www.sciencedirect.com/science/article/pii/S0010465511003936
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: Amparo Gil and Javier Segura and Nico M. Temme
title:
An improved algorithm and a Fortran 90 module for computing the conical function $ p^m_1 / 2 + i tau (x) $

bibsource:
https://www.math.utah.edu/pub/tex/bib/compphyscomm2010.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

rawtitle:
An improved algorithm and a {Fortran 90} module for computing the conical function $ p^m_{1 / 2 + i \tau }(x) $

entry:
@Article{Gil:2012:IAF,
  author =       "Amparo Gil and Javier Segura and Nico M. Temme",
  title =        "An improved algorithm and a {Fortran 90} module for
                 computing the conical function $ p^m_{1 / 2 + i \tau
                 }(x) $",
  journal =      j-COMP-PHYS-COMM,
  volume =       "183",
  number =       "3",
  pages =        "794--799",
  month =        mar,
  year =         "2012",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/j.cpc.2011.11.025",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Sat Feb 11 10:11:02 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465511003936",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}


bibtype: article
filename: elefunt.bib
label: Jablonski:2012:EAC
author: A. Jablonski
title: An effective algorithm for calculating the Chandrasekhar function
journal: j-COMP-PHYS-COMM
volume: 183
number: 8
pages: 1773--1782
month: aug
monthnumber: 8
year: 2012
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/j.cpc.2012.02.022
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Tue Apr 24 06:33:31 MDT 2012
bibtimestamp: 2012.04.24 06:33:31 MDT
URL: http://www.sciencedirect.com/science/article/pii/S0010465512000847
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: A. Jablonski
rawtitle: An effective algorithm for calculating the {Chandrasekhar} function
bibsource:
https://www.math.utah.edu/pub/tex/bib/compphyscomm2010.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Jablonski:2012:EAC,
  author =       "A. Jablonski",
  title =        "An effective algorithm for calculating the
                 {Chandrasekhar} function",
  journal =      j-COMP-PHYS-COMM,
  volume =       "183",
  number =       "8",
  pages =        "1773--1782",
  month =        aug,
  year =         "2012",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/j.cpc.2012.02.022",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Tue Apr 24 06:33:31 MDT 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465512000847",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}


bibtype: incollection
filename: elefunt.bib
label: Jargstorff:2012:AEF
author: Frank Jargstorff
title: Approximating the tt erfinv Function
crossref: Hwu:2012:GCG
chapter: 10
pages: ??--??
year: 2012
bibdate: Sat Feb 08 19:05:23 2014
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2014.02.08 19:05:23 ???
acknowledgement: ack-nhfb
rawauthor: Frank Jargstorff
rawtitle: Approximating the {{\tt erfinv}} Function
entry:
@InCollection{Jargstorff:2012:AEF,
  author =       "Frank Jargstorff",
  title =        "Approximating the {{\tt erfinv}} Function",
  crossref =     "Hwu:2012:GCG",
  chapter =      "10",
  pages =        "??--??",
  year =         "2012",
  bibdate =      "Sat Feb 08 19:05:23 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Jentschura:2012:NCB
author: U. D. Jentschura and E. Lotstedt
title: Numerical calculation of Bessel, Hankel and Airy functions
journal: j-COMP-PHYS-COMM
volume: 183
number: 3
pages: 506--519
month: mar
monthnumber: 3
year: 2012
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/j.cpc.2011.11.010
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Sat Feb 11 10:11:02 MST 2012
bibtimestamp: 2012.02.11 10:11:02 MST
URL: http://www.sciencedirect.com/science/article/pii/S0010465511003729
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: U. D. Jentschura and E. L{\"o}tstedt
rawtitle: Numerical calculation of {Bessel}, {Hankel} and {Airy} functions
entry:
@Article{Jentschura:2012:NCB,
  author =       "U. D. Jentschura and E. L{\"o}tstedt",
  title =        "Numerical calculation of {Bessel}, {Hankel} and {Airy}
                 functions",
  journal =      j-COMP-PHYS-COMM,
  volume =       "183",
  number =       "3",
  pages =        "506--519",
  month =        mar,
  year =         "2012",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/j.cpc.2011.11.010",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Sat Feb 11 10:11:02 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465511003729",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}


bibtype: misc
filename: elefunt.bib
label: Johnson:2012:FPF
author: Steven G. Johnson
pages: 506--519
year: 2012
bibdate: Sat Feb 17 14:11:45 2024
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2024.02.17 14:11:45 ???
URL: http://ab-initio.mit.edu/wiki/index.php/Faddeeva_Package
acknowledgement: ack-nhfb
howpublished: Web site
rawauthor: Steven G. Johnson
title:
Faddeeva package, a free / open-source C++ Software to compute the various error functions of arbitrary complex arguments

keywords:
$erf (x) (the error function); $erfc () (complementary error function = $1 - erf (z)$); $erfcx () (scaled complementary error function $e^z^2 erfc (z) = w(i z)$); $erfi (z) (imaginary error function = $-i erf (i z)$); Dawson ($((sqrt pi )/2) e^-z^2 erfi (z)$); w (Faddeeva function $w(z) = e^-z^2 erfc (-i z)$)

rawtitle:
{Faddeeva} package, a free\slash open-source {C++} Software to compute the various error functions of arbitrary complex arguments

entry:
@Misc{Johnson:2012:FPF,
  author =       "Steven G. Johnson",
  title =        "{Faddeeva} package, a free\slash open-source {C++}
                 Software to compute the various error functions of
                 arbitrary complex arguments",
  howpublished = "Web site",
  year =         "2012",
  bibdate =      "Sat Feb 17 14:11:45 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://ab-initio.mit.edu/wiki/index.php/Faddeeva_Package",
  acknowledgement = ack-nhfb,
  keywords =     "$\erf(x) (the error function); $\erfc() (complementary
                 error function = $1 - \erf(z)$); $\erfcx() (scaled
                 complementary error function $e^{z^2} \erfc(z) = w(i
                 z)$); $\erfi(z) (imaginary error function = $-i \erf(i
                 z)$); Dawson ($((\sqrt \pi)/2) e^{-z^2} \erfi(z)$); w
                 (Faddeeva function $w(z) = e^{-z^2} \erfc(-i z)$)",
}


bibtype: inproceedings
filename: elefunt.bib
label: Phong:2012:EAG
author: Dao Ngoc Phong and Nguyen Quang Uy and Nguyen Xuan Hoai and R. I. (Bob) McKay
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 1--6
year: 2012
DOI: https://doi.org/10.1109/CEC.2012.6256588
bibdate: Sat Dec 16 16:08:39 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.12.16 16:08:39 ???
URL: http://ieeexplore.ieee.org/document/6256588/
acknowledgement: ack-nhfb
rawauthor: Dao Ngoc Phong and Nguyen Quang Uy and Nguyen Xuan Hoai and R. I. (Bob) McKay
booktitle:
Proceedings of the 2012 IEEE Congress on Evolutionary Computation, June 10--15, 2012 --- Brisbane, QLD, Australia

title:
Evolving approximations for the Gaussian $Q$-function by genetic programming with semantic based crossover

rawbooktitle:
Proceedings of the 2012 {IEEE} Congress on Evolutionary Computation, June 10--15, 2012 --- Brisbane, {QLD}, Australia

rawtitle:
Evolving approximations for the {Gaussian} {$Q$}-function by genetic programming with semantic based crossover

entry:
@InProceedings{Phong:2012:EAG,
  author =       "Dao Ngoc Phong and Nguyen Quang Uy and Nguyen Xuan
                 Hoai and R. I. (Bob) McKay",
  editor =       "????",
  booktitle =    "Proceedings of the 2012 {IEEE} Congress on
                 Evolutionary Computation, June 10--15, 2012 ---
                 Brisbane, {QLD}, Australia",
  title =        "Evolving approximations for the {Gaussian}
                 {$Q$}-function by genetic programming with semantic
                 based crossover",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--6",
  year =         "2012",
  DOI =          "https://doi.org/10.1109/CEC.2012.6256588",
  bibdate =      "Sat Dec 16 16:08:39 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://ieeexplore.ieee.org/document/6256588/",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Poelke:2012:DCC
author: Konstantin Poelke and Konrad Polthier
title: Domain Coloring of Complex Functions: An Implementation-Oriented Introduction
journal: j-IEEE-CGA
volume: 32
number: 5
pages: 90--97
month: sep
monthnumber: 9
year: 2012
CODEN: ICGADZ
DOI: https://doi.org/10.1109/MCG.2012.100
ISSN: 0272-1716 (print), 1558-1756 (electronic) OR 02721716 (print), 15581756 (electronic)
ISSNL: 0272-1716 OR 02721716
bibdate: Mon Oct 22 06:56:23 2012
bibtimestamp: 2012.10.22 06:56:23 ???
fjournal: IEEE Computer Graphics and Applications
acknowledgement: ack-nhfb
journalURL: http://www.computer.org/portal/web/csdl/magazines/cga
rawauthor: Konstantin Poelke and Konrad Polthier
rawtitle: Domain Coloring of Complex Functions: An Implementation-Oriented Introduction
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/ieeecga.bib

entry:
@Article{Poelke:2012:DCC,
  author =       "Konstantin Poelke and Konrad Polthier",
  title =        "Domain Coloring of Complex Functions: An
                 Implementation-Oriented Introduction",
  journal =      j-IEEE-CGA,
  volume =       "32",
  number =       "5",
  pages =        "90--97",
  month =        sep # "\slash " # oct,
  year =         "2012",
  CODEN =        "ICGADZ",
  DOI =          "https://doi.org/10.1109/MCG.2012.100",
  ISSN =         "0272-1716 (print), 1558-1756 (electronic)",
  ISSN-L =       "0272-1716",
  bibdate =      "Mon Oct 22 06:56:23 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeecga.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Computer Graphics and Applications",
  journal-URL =  "http://www.computer.org/portal/web/csdl/magazines/cga",
}


bibtype: article
filename: elefunt.bib
label: Rzadkowski:2012:SEE
author: Grzegorz Rzadkowski
title: On some expansions for the Euler Gamma function and the Riemann Zeta function
journal: j-J-COMPUT-APPL-MATH
volume: 236
number: 15
pages: 3710--3719
month: sep
monthnumber: 9
year: 2012
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 13:24:35 MST 2017
bibtimestamp: 2017.02.25 13:24:35 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042711004663
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Grzegorz Rz{\k{a}}dkowski
rawtitle: On some expansions for the {Euler} Gamma function and the {Riemann} Zeta function
entry:
@Article{Rzadkowski:2012:SEE,
  author =       "Grzegorz Rz{\k{a}}dkowski",
  title =        "On some expansions for the {Euler} Gamma function and
                 the {Riemann} Zeta function",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "236",
  number =       "15",
  pages =        "3710--3719",
  month =        sep,
  year =         "2012",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 13:24:35 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2010.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042711004663",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: book
filename: elefunt.bib
label: Srivastava:2012:ZZF
author: H. M. Srivastava and Choi Junesang
title: Zeta and $q$-Zeta functions and associated series and integrals
publisher: pub-ELSEVIER
address: pub-ELSEVIER:adr
pages: xvi + 657
year: 2012
ISBN: 0-12-385218-8 OR 0123852188
ISBN13: 978-0-12-385218-2 OR 9780123852182
LCCN: QA351 .S745 2012
bibdate: Wed Jun 10 16:19:46 MDT 2015
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2015.06.10 16:19:46 MDT
series: Elsevier Insights
URL: http://www.sciencedirect.com/science/book/9780123852182
remark: Revised, enlarged, and updated version of cite Srivastava:2001:SAZ.
subject: Functions, Zeta
acknowledgement: ack-nhfb
rawauthor: H. M. Srivastava and Choi Junesang
rawtitle: Zeta and $q$-Zeta functions and associated series and integrals
TOC:
1. Introduction and preliminaries 2. The zeta and related functions 3. Series involving zeta functions 4. Evaluations and series representations 5. Determinants of the laplacians 6. q-Extensions of some special functions and polynomials 7. Miscellaneous results

rawTOC:
1. Introduction and preliminaries \\ 2. The zeta and related functions \\ 3. Series involving zeta functions \\ 4. Evaluations and series representations \\ 5. Determinants of the laplacians \\ 6. q-Extensions of some special functions and polynomials \\ 7. Miscellaneous results

entry:
@Book{Srivastava:2012:ZZF,
  author =       "H. M. Srivastava and Choi Junesang",
  title =        "Zeta and $q$-Zeta functions and associated series and
                 integrals",
  publisher =    pub-ELSEVIER,
  address =      pub-ELSEVIER:adr,
  pages =        "xvi + 657",
  year =         "2012",
  ISBN =         "0-12-385218-8",
  ISBN-13 =      "978-0-12-385218-2",
  LCCN =         "QA351 .S745 2012",
  bibdate =      "Wed Jun 10 16:19:46 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Elsevier Insights",
  URL =          "http://www.sciencedirect.com/science/book/9780123852182",
  acknowledgement = ack-nhfb,
  remark =       "Revised, enlarged, and updated version of
                 \cite{Srivastava:2001:SAZ}.",
  subject =      "Functions, Zeta",
  tableofcontents = "1. Introduction and preliminaries \\
                 2. The zeta and related functions \\
                 3. Series involving zeta functions \\
                 4. Evaluations and series representations \\
                 5. Determinants of the laplacians \\
                 6. q-Extensions of some special functions and
                 polynomials \\
                 7. Miscellaneous results",
}


bibtype: article
filename: elefunt.bib
label: Vazquez-Leal:2012:HAS
title: High Accurate Simple Approximation of Normal Distribution Integral
journal: Mathematical Problems in Engineering
volume: 2012
pages: 1--22
year: 2012
DOI: https://doi.org/10.1155/2012/124029
ISSN: 1024-123X (print), 1563-5147 (electronic) OR 1024123X (print), 15635147 (electronic)
bibdate: Sat Dec 16 17:54:09 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.12.16 17:54:09 ???
URL: https://www.hindawi.com/journals/mpe/2012/124029/
acknowledgement: ack-nhfb
rawtitle: High Accurate Simple Approximation of Normal Distribution Integral
author:
Hector Vazquez-Leal and Roberto Castaneda-Sheissa and Uriel Filobello-Nino and Arturo Sarmiento-Reyes and Jesus Sanchez Orea

rawauthor:
Hector Vazquez-Leal and Roberto Castaneda-Sheissa and Uriel Filobello-Nino and Arturo Sarmiento-Reyes and Jesus Sanchez Orea

entry:
@Article{Vazquez-Leal:2012:HAS,
  author =       "Hector Vazquez-Leal and Roberto Castaneda-Sheissa and
                 Uriel Filobello-Nino and Arturo Sarmiento-Reyes and
                 Jesus Sanchez Orea",
  title =        "High Accurate Simple Approximation of Normal
                 Distribution Integral",
  journal =      "Mathematical Problems in Engineering",
  volume =       "2012",
  pages =        "1--22",
  year =         "2012",
  DOI =          "https://doi.org/10.1155/2012/124029",
  ISSN =         "1024-123X (print), 1563-5147 (electronic)",
  bibdate =      "Sat Dec 16 17:54:09 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://www.hindawi.com/journals/mpe/2012/124029/",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Veberic:2012:LFA
author: Darko Veberic
title: Lambert $W$ function for applications in physics
journal: j-COMP-PHYS-COMM
volume: 183
number: 12
pages: 2622--2628
month: dec
monthnumber: 12
year: 2012
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/j.cpc.2012.07.008
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Tue Aug 28 17:36:53 MDT 2012
bibtimestamp: 2012.08.28 17:36:53 MDT
URL: http://www.sciencedirect.com/science/article/pii/S0010465512002366
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: Darko Veberi{\v{c}}
rawtitle: {Lambert} {$W$} function for applications in physics
entry:
@Article{Veberic:2012:LFA,
  author =       "Darko Veberi{\v{c}}",
  title =        "{Lambert} {$W$} function for applications in physics",
  journal =      j-COMP-PHYS-COMM,
  volume =       "183",
  number =       "12",
  pages =        "2622--2628",
  month =        dec,
  year =         "2012",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/j.cpc.2012.07.008",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Tue Aug 28 17:36:53 MDT 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465512002366",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}


bibtype: article
filename: elefunt.bib
label: Willis:2012:AGH
author: Joshua L. Willis
title: Acceleration of generalized hypergeometric functions through precise remainder asymptotics
journal: j-NUMER-ALGORITHMS
volume: 59
pages: ??--??
year: 2012
CODEN: NUALEG
DOI: https://doi.org/10.1007/s11075-011-9499-9
ISSN: 1017-1398 (print), 1572-9265 (electronic) OR 10171398 (print), 15729265 (electronic)
ISSNL: 1017-1398 OR 10171398
bibdate: Wed Nov 30 06:42:07 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2011.11.30 06:42:07 ???
URL: http://arxiv.org/abs/1102.3003; http://www.springerlink.com/content/k413064448600815/
fjournal: Numerical Algorithms
keywords: Generalized hypergeometric functions; Recurrence asymptotics; Series acceleration
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/11075
rawauthor: Joshua L. Willis
rawtitle: Acceleration of generalized hypergeometric functions through precise remainder asymptotics
abstract:
We express the asymptotics of the remainders of the partial sums $ s_n $ of the generalized hypergeometric function through an inverse power series $ z^n n^lambda sum c_k / n_k $, where the exponent $ lambda $ and the asymptotic coefficients $ c_k $ may be recursively computed to any desired order from the hypergeometric parameters and argument. From this we derive a new series acceleration technique that can be applied to any such function, even with complex parameters and at the branch point $ z = 1 $. For moderate parameters (up to approximately ten) a C implementation at fixed precision is very effective at computing these functions; for larger parameters an implementation in higher than machine precision would be needed. Even for larger parameters, however, our C implementation is able to correctly determine whether or not it has converged; and when it converges, its estimate of its error is accurate.

rawabstract:
We express the asymptotics of the remainders of the partial sums $ \{ s_n \} $ of the generalized hypergeometric function through an inverse power series $ z^n n^\lambda \sum c_k / n_k $, where the exponent $ \lambda $ and the asymptotic coefficients $ \{ c_k \} $ may be recursively computed to any desired order from the hypergeometric parameters and argument. From this we derive a new series acceleration technique that can be applied to any such function, even with complex parameters and at the branch point $ z = 1 $. For moderate parameters (up to approximately ten) a C implementation at fixed precision is very effective at computing these functions; for larger parameters an implementation in higher than machine precision would be needed. Even for larger parameters, however, our C implementation is able to correctly determine whether or not it has converged; and when it converges, its estimate of its error is accurate.

entry:
@Article{Willis:2012:AGH,
  author =       "Joshua L. Willis",
  title =        "Acceleration of generalized hypergeometric functions
                 through precise remainder asymptotics",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "59",
  number =       "??",
  pages =        "??--??",
  month =        "????",
  year =         "2012",
  CODEN =        "NUALEG",
  DOI =          "https://doi.org/10.1007/s11075-011-9499-9",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Wed Nov 30 06:42:07 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://arxiv.org/abs/1102.3003;
                 http://www.springerlink.com/content/k413064448600815/",
  abstract =     "We express the asymptotics of the remainders of the
                 partial sums $ \{ s_n \} $ of the generalized
                 hypergeometric function through an inverse power series
                 $ z^n n^\lambda \sum c_k / n_k $, where the exponent $
                 \lambda $ and the asymptotic coefficients $ \{ c_k \} $
                 may be recursively computed to any desired order from
                 the hypergeometric parameters and argument. From this
                 we derive a new series acceleration technique that can
                 be applied to any such function, even with complex
                 parameters and at the branch point $ z = 1 $. For
                 moderate parameters (up to approximately ten) a C
                 implementation at fixed precision is very effective at
                 computing these functions; for larger parameters an
                 implementation in higher than machine precision would
                 be needed. Even for larger parameters, however, our C
                 implementation is able to correctly determine whether
                 or not it has converged; and when it converges, its
                 estimate of its error is accurate.",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
  keywords =     "Generalized hypergeometric functions; Recurrence
                 asymptotics; Series acceleration",
}


bibtype: incollection
filename: elefunt.bib
label: Arfken:2013:BF
author: George B. (George Brown) Arfken and Hans-Jurgen Weber and Frank E. Harris
title: Bessel Functions
crossref: Arfken:2013:MMP
chapter: 14
pages: 643--713
year: 2013
bibdate: Thu Dec 5 05:54:14 MST 2013
bibtimestamp: 2013.12.05 05:54:14 MST
URL: http://www.sciencedirect.com/science/article/pii/B9780123846549000141
acknowledgement: ack-nhfb
rawauthor: George B. (George Brown) Arfken and Hans-J{\"u}rgen Weber and Frank E. Harris
rawtitle: {Bessel} Functions
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/h/harris-frank-e.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@InCollection{Arfken:2013:BF,
  author =       "George B. (George Brown) Arfken and Hans-J{\"u}rgen
                 Weber and Frank E. Harris",
  title =        "{Bessel} Functions",
  crossref =     "Arfken:2013:MMP",
  chapter =      "14",
  pages =        "643--713",
  year =         "2013",
  bibdate =      "Thu Dec 5 05:54:14 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/harris-frank-e.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/B9780123846549000141",
  acknowledgement = ack-nhfb,
}


bibtype: incollection
filename: elefunt.bib
label: Arfken:2013:GFb
author: George B. (George Brown) Arfken and Hans-Jurgen Weber and Frank E. Harris
title: Gamma Function
crossref: Arfken:2013:MMP
chapter: 13
pages: 599--641
year: 2013
bibdate: Thu Dec 5 05:54:14 MST 2013
bibtimestamp: 2013.12.05 05:54:14 MST
URL: http://www.sciencedirect.com/science/article/pii/B978012384654900013X
acknowledgement: ack-nhfb
rawauthor: George B. (George Brown) Arfken and Hans-J{\"u}rgen Weber and Frank E. Harris
rawtitle: {Gamma} Function
entry:
@InCollection{Arfken:2013:GFb,
  author =       "George B. (George Brown) Arfken and Hans-J{\"u}rgen
                 Weber and Frank E. Harris",
  title =        "{Gamma} Function",
  crossref =     "Arfken:2013:MMP",
  chapter =      "13",
  pages =        "599--641",
  year =         "2013",
  bibdate =      "Thu Dec 5 05:54:14 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/harris-frank-e.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/B978012384654900013X",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Babusci:2013:SME
author: D. Babusci and G. Dattoli and K. Gorska and K. A. Penson
title: Symbolic methods for the evaluation of sum rules of Bessel functions
journal: j-J-MATH-PHYS
volume: 54
number: 7
pages: 073501
month: jul
monthnumber: 7
year: 2013
CODEN: JMAPAQ
DOI: https://doi.org/10.1063/1.4812325
ISSNL: 0022-2488 OR 00222488
bibdate: Wed Feb 12 12:24:18 MST 2014
bibtimestamp: 2014.02.12 12:24:18 MST
fjournal: Journal of Mathematical Physics
acknowledgement: ack-nhfb
journalURL: http://jmp.aip.org/
rawauthor: D. Babusci and G. Dattoli and K. G{\'o}rska and K. A. Penson
rawtitle: Symbolic methods for the evaluation of sum rules of {Bessel} functions
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jmathphys2010.bib

entry:
@Article{Babusci:2013:SME,
  author =       "D. Babusci and G. Dattoli and K. G{\'o}rska and K. A.
                 Penson",
  title =        "Symbolic methods for the evaluation of sum rules of
                 {Bessel} functions",
  journal =      j-J-MATH-PHYS,
  volume =       "54",
  number =       "7",
  pages =        "073501",
  month =        jul,
  year =         "2013",
  CODEN =        "JMAPAQ",
  DOI =          "https://doi.org/10.1063/1.4812325",
  ISSN =         "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
  ISSN-L =       "0022-2488",
  bibdate =      "Wed Feb 12 12:24:18 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jmathphys2010.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Physics",
  journal-URL =  "http://jmp.aip.org/",
}


bibtype: article
filename: elefunt.bib
label: Booker:2013:BAB
author: Andrew R. Booker and Andreas Strombergsson and Holger Then
title: Bounds and algorithms for the $K$-Bessel function of imaginary order
journal: j-LMS-J-COMPUT-MATH
volume: 16
pages: 78--108
year: 2013
DOI: https://doi.org/10.1112/S1461157013000028
ISSN: 1461-1570 OR 14611570
ISSNL: 1461-1570 OR 14611570
MRclass: 26D07; 33C10; 33F05; 34D05; 41A58 (primary); 41A80; 65D05; 40H05; 26B99 (secondary)
bibdate: Sat Jun 22 11:29:28 MDT 2013
bibtimestamp: 2013.06.22 11:29:28 MDT
fjournal: LMS Journal of Computation and Mathematics
acknowledgement: ack-nhfb
ajournal: LMS J. Comput. Math.
journalURL: http://journals.cambridge.org/action/displayJournal?jid=JCM
onlinedate: 10 April 2013
rawauthor: Andrew R. Booker and Andreas Str{\"o}mbergsson and Holger Then
rawtitle: Bounds and algorithms for the {$K$-Bessel} function of imaginary order
bibsource:
http://journals.cambridge.org/action/displayJournal?jid=JCM; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/lms-j-comput-math.bib

entry:
@Article{Booker:2013:BAB,
  author =       "Andrew R. Booker and Andreas Str{\"o}mbergsson and
                 Holger Then",
  title =        "Bounds and algorithms for the {$K$-Bessel} function of
                 imaginary order",
  journal =      j-LMS-J-COMPUT-MATH,
  volume =       "16",
  pages =        "78--108",
  year =         "2013",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1112/S1461157013000028",
  ISSN =         "1461-1570",
  ISSN-L =       "1461-1570",
  MRclass =      "26D07; 33C10; 33F05; 34D05; 41A58 (primary); 41A80;
                 65D05; 40H05; 26B99 (secondary)",
  bibdate =      "Sat Jun 22 11:29:28 MDT 2013",
  bibsource =    "http://journals.cambridge.org/action/displayJournal?jid=JCM;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/lms-j-comput-math.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "LMS J. Comput. Math.",
  fjournal =     "LMS Journal of Computation and Mathematics",
  journal-URL =  "http://journals.cambridge.org/action/displayJournal?jid=JCM",
  onlinedate =   "10 April 2013",
}


bibtype: article
filename: elefunt.bib
label: Chen:2013:CFE
author: Chao-Ping Chen
title: Continued fraction estimates for the psi function
journal: j-APPL-MATH-COMP
volume: 219
number: 19
pages: 9865--9871
day: 1
month: jun
monthnumber: 6
year: 2013
CODEN: AMHCBQ
DOI: https://doi.org/10.1016/j.amc.2013.03.134
ISSN: 0096-3003 (print), 1873-5649 (electronic) OR 00963003 (print), 18735649 (electronic)
ISSNL: 0096-3003 OR 00963003
bibdate: Mon May 20 19:05:31 MDT 2013
bibtimestamp: 2013.05.20 19:05:31 MDT
URL: http://www.sciencedirect.com/science/article/pii/S0096300313003962
fjournal: Applied Mathematics and Computation
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00963003
rawauthor: Chao-Ping Chen
rawtitle: Continued fraction estimates for the psi function
bibsource:
http://www.sciencedirect.com/science/journal/00963003; https://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/mathcw.bib

entry:
@Article{Chen:2013:CFE,
  author =       "Chao-Ping Chen",
  title =        "Continued fraction estimates for the psi function",
  journal =      j-APPL-MATH-COMP,
  volume =       "219",
  number =       "19",
  pages =        "9865--9871",
  day =          "1",
  month =        jun,
  year =         "2013",
  CODEN =        "AMHCBQ",
  DOI =          "https://doi.org/10.1016/j.amc.2013.03.134",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Mon May 20 19:05:31 MDT 2013",
  bibsource =    "http://www.sciencedirect.com/science/journal/00963003;
                 https://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0096300313003962",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
}


bibtype: article
filename: elefunt.bib
label: Chen:2013:LIA
author: Chao-Ping Chen and Cristinel Mortici
title: Limits and inequalities associated with the Euler--Mascheroni constant
journal: j-APPL-MATH-COMP
volume: 219
number: 18
pages: 9755--9761
day: 15
month: may
monthnumber: 5
year: 2013
CODEN: AMHCBQ
DOI: https://doi.org/10.1016/j.amc.2013.03.089
ISSN: 0096-3003 (print), 1873-5649 (electronic) OR 00963003 (print), 18735649 (electronic)
ISSNL: 0096-3003 OR 00963003
bibdate: Mon May 20 19:05:27 MDT 2013
bibtimestamp: 2013.05.20 19:05:27 MDT
URL: http://www.sciencedirect.com/science/article/pii/S0096300313003500
fjournal: Applied Mathematics and Computation
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00963003
rawauthor: Chao-Ping Chen and Cristinel Mortici
rawtitle: Limits and inequalities associated with the {Euler--Mascheroni} constant
keywords:
asymptotic expansion; Euler-Mascheroni constant; harmonic numbers; inequality; polygamma functions; psi function

entry:
@Article{Chen:2013:LIA,
  author =       "Chao-Ping Chen and Cristinel Mortici",
  title =        "Limits and inequalities associated with the
                 {Euler--Mascheroni} constant",
  journal =      j-APPL-MATH-COMP,
  volume =       "219",
  number =       "18",
  pages =        "9755--9761",
  day =          "15",
  month =        may,
  year =         "2013",
  CODEN =        "AMHCBQ",
  DOI =          "https://doi.org/10.1016/j.amc.2013.03.089",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Mon May 20 19:05:27 MDT 2013",
  bibsource =    "http://www.sciencedirect.com/science/journal/00963003;
                 https://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0096300313003500",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
  keywords =     "asymptotic expansion; Euler-Mascheroni constant;
                 harmonic numbers; inequality; polygamma functions; psi
                 function",
}


bibtype: article
filename: elefunt.bib
label: Chen:2013:UTS
author: Chao-Ping Chen
title: Unified treatment of several asymptotic formulas for the gamma function
journal: j-NUMER-ALGORITHMS
volume: 64
number: 2
pages: 311--319
month: oct
monthnumber: 10
year: 2013
CODEN: NUALEG
DOI: https://doi.org/10.1007/s11075-012-9667-6
ISSN: 1017-1398 (print), 1572-9265 (electronic) OR 10171398 (print), 15729265 (electronic)
ISSNL: 1017-1398 OR 10171398
bibdate: Mon Dec 2 18:18:08 MST 2013
bibtimestamp: 2013.12.02 18:18:08 MST
URL: http://link.springer.com/article/10.1007/s11075-012-9667-6
fjournal: Numerical Algorithms
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/11075
rawauthor: Chao-Ping Chen
rawtitle: Unified treatment of several asymptotic formulas for the gamma function
bibsource:
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1017-1398&volume=64&issue=2; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib

entry:
@Article{Chen:2013:UTS,
  author =       "Chao-Ping Chen",
  title =        "Unified treatment of several asymptotic formulas for
                 the gamma function",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "64",
  number =       "2",
  pages =        "311--319",
  month =        oct,
  year =         "2013",
  CODEN =        "NUALEG",
  DOI =          "https://doi.org/10.1007/s11075-012-9667-6",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Mon Dec 2 18:18:08 MST 2013",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1017-1398&volume=64&issue=2;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
  URL =          "http://link.springer.com/article/10.1007/s11075-012-9667-6",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
}


bibtype: inproceedings
filename: elefunt.bib
label: Chevillard:2013:MPE
author: Sylvain Chevillard and Marc Mezzarobba
title: Multiple-Precision Evaluation of the Airy Ai Function with Reduced Cancellation
crossref: IEEE:2013:PIS
pages: 175--182
year: 2013
DOI: https://doi.org/10.1109/ARITH.2013.33
ISSN: 1063-6889 OR 10636889
bibdate: Sat Aug 1 09:38:32 2015
bibtimestamp: 2015.08.01 09:38:32 ???
acknowledgement: ack-nhfb
rawauthor: Sylvain Chevillard and Marc Mezzarobba
rawtitle: Multiple-Precision Evaluation of the {Airy} {Ai} Function with Reduced Cancellation
keywords:
Accuracy; Airy Ai function; algorithm; Algorithm design and analysis; Approximation algorithms; Approximation methods; arbitrary precision; ARITH-21; asymptotics; cancellation reduction; classical Miller algorithm; correct rounding; differential equations; Equations; error bounds; ill-conditioned three-term recurrence; linear ordinary differential equation; Miller method; multiple-precision evaluation; nonnegative Taylor expansions; numerical evaluation; series (mathematics); series expansion; Shape; Special functions; Taylor coefficients; Taylor series

entry:
@InProceedings{Chevillard:2013:MPE,
  author =       "Sylvain Chevillard and Marc Mezzarobba",
  title =        "Multiple-Precision Evaluation of the {Airy} {Ai}
                 Function with Reduced Cancellation",
  crossref =     "IEEE:2013:PIS",
  pages =        "175--182",
  year =         "2013",
  DOI =          "https://doi.org/10.1109/ARITH.2013.33",
  ISSN =         "1063-6889",
  bibdate =      "Sat Aug 1 09:38:32 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Accuracy; Airy Ai function; algorithm; Algorithm
                 design and analysis; Approximation algorithms;
                 Approximation methods; arbitrary precision; ARITH-21;
                 asymptotics; cancellation reduction; classical Miller
                 algorithm; correct rounding; differential equations;
                 Equations; error bounds; ill-conditioned three-term
                 recurrence; linear ordinary differential equation;
                 Miller method; multiple-precision evaluation;
                 nonnegative Taylor expansions; numerical evaluation;
                 series (mathematics); series expansion; Shape; Special
                 functions; Taylor coefficients; Taylor series",
}


bibtype: article
filename: elefunt.bib
label: deDinechin:2013:FPT
author: Florent de Dinechin and Matei Istoan and Guillaume Sergent
title: Fixed-point trigonometric functions on FPGAs
journal: j-COMP-ARCH-NEWS
volume: 41
number: 5
pages: 83--88
month: dec
monthnumber: 12
year: 2013
CODEN: CANED2
DOI: https://doi.org/10.1145/2641361.2641375
ISSN: 0163-5964 (print), 1943-5851 (electronic) OR 01635964 (print), 19435851 (electronic)
ISSNL: 0163-5964 OR 01635964
bibdate: Mon Aug 18 17:12:43 MDT 2014
bibtimestamp: 2014.08.18 17:12:43 MDT
fjournal: ACM SIGARCH Computer Architecture News
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J89
rawauthor: Florent de Dinechin and Matei Istoan and Guillaume Sergent
rawtitle: Fixed-point trigonometric functions on {FPGAs}
bibsource:
http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/sigarch.bib

abstract:
Three approaches for computing sines and cosines on FPGAs are studied in this paper, with a focus of high-throughput pipelined architecture, and state-of-the-art implementation techniques. The first approach is the classical CORDIC iteration, for which we suggest a reduced iteration technique and fine optimizations in datapath width and latency. The second is an ad-hoc architecture specifically designed around trigonometric identities. The third uses a generic table- and DSP-based polynomial approximator. These three architectures are implemented and compared in the FloPoCo framework.

rawabstract:
Three approaches for computing sines and cosines on FPGAs are studied in this paper, with a focus of high-throughput pipelined architecture, and state-of-the-art implementation techniques. The first approach is the classical CORDIC iteration, for which we suggest a reduced iteration technique and fine optimizations in datapath width and latency. The second is an ad-hoc architecture specifically designed around trigonometric identities. The third uses a generic table- and DSP-based polynomial approximator. These three architectures are implemented and compared in the FloPoCo framework.

entry:
@Article{deDinechin:2013:FPT,
  author =       "Florent de Dinechin and Matei Istoan and Guillaume
                 Sergent",
  title =        "Fixed-point trigonometric functions on {FPGAs}",
  journal =      j-COMP-ARCH-NEWS,
  volume =       "41",
  number =       "5",
  pages =        "83--88",
  month =        dec,
  year =         "2013",
  CODEN =        "CANED2",
  DOI =          "https://doi.org/10.1145/2641361.2641375",
  ISSN =         "0163-5964 (print), 1943-5851 (electronic)",
  ISSN-L =       "0163-5964",
  bibdate =      "Mon Aug 18 17:12:43 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigarch.bib",
  abstract =     "Three approaches for computing sines and cosines on
                 FPGAs are studied in this paper, with a focus of
                 high-throughput pipelined architecture, and
                 state-of-the-art implementation techniques. The first
                 approach is the classical CORDIC iteration, for which
                 we suggest a reduced iteration technique and fine
                 optimizations in datapath width and latency. The second
                 is an ad-hoc architecture specifically designed around
                 trigonometric identities. The third uses a generic
                 table- and DSP-based polynomial approximator. These
                 three architectures are implemented and compared in the
                 FloPoCo framework.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGARCH Computer Architecture News",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J89",
}


bibtype: article
filename: elefunt.bib
label: Develi:2013:HAA
author: I. Develi and A. Basturk
journal: j-J-OPT-THEORY-APPL
volume: 159
number: 1
pages: 183--191
day: 01
month: oct
monthnumber: 10
year: 2013
CODEN: JOTABN
DOI: https://doi.org/10.1007/s10957-012-0217-0
ISSN: 1573-2878 OR 15732878
ISSNL: 0022-3239 OR 00223239
bibdate: Sat Dec 16 16:18:18 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.12.16 16:18:18 ???
URL: https://link.springer.com/article/10.1007/s10957-012-0217-0
fjournal: Journal of Optimization Theory and Applications
acknowledgement: ack-nhfb
ajournal: J. Optim. Theory Appl.
journalURL: http://link.springer.com/journal/volumesAndIssues/10957
rawauthor: I. Develi and A. Basturk
title:
Highly Accurate Analytic Approximation to the Gaussian $Q$-function Based on the Use of Nonlinear Least Squares Optimization Algorithm

rawtitle:
Highly Accurate Analytic Approximation to the {Gaussian} {$Q$}-function Based on the Use of Nonlinear Least Squares Optimization Algorithm

entry:
@Article{Develi:2013:HAA,
  author =       "I. Develi and A. Basturk",
  title =        "Highly Accurate Analytic Approximation to the
                 {Gaussian} {$Q$}-function Based on the Use of Nonlinear
                 Least Squares Optimization Algorithm",
  journal =      j-J-OPT-THEORY-APPL,
  volume =       "159",
  number =       "1",
  pages =        "183--191",
  day =          "01",
  month =        oct,
  year =         "2013",
  CODEN =        "JOTABN",
  DOI =          "https://doi.org/10.1007/s10957-012-0217-0",
  ISSN =         "1573-2878",
  ISSN-L =       "0022-3239",
  bibdate =      "Sat Dec 16 16:18:18 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://link.springer.com/article/10.1007/s10957-012-0217-0",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Optim. Theory Appl.",
  fjournal =     "Journal of Optimization Theory and Applications",
  journal-URL =  "http://link.springer.com/journal/volumesAndIssues/10957",
}


bibtype: article
filename: elefunt.bib
label: Erricolo:2013:AFS
author: Danilo Erricolo and Giuseppe Carluccio
journal: j-TOMS
volume: 40
number: 1
pages: 8:1--8:19
month: sep
monthnumber: 9
year: 2013
CODEN: ACMSCU
DOI: https://doi.org/10.1145/2513109.2513117
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Mon Sep 30 16:05:58 MDT 2013
bibtimestamp: 2013.09.30 16:05:58 MDT
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
articleno: 8
journalURL: https://dl.acm.org/loi/toms
rawauthor: Danilo Erricolo and Giuseppe Carluccio
title:
Algorithm 934: Fortran 90 subroutines to compute Mathieu functions for complex values of the parameter

bibsource:
http://www.acm.org/pubs/contents/journals/toms/; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fortran3.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib

abstract:
Software to compute angular and radial Mathieu functions is provided in the case that the parameter q is a complex variable and the independent variable x is real. After an introduction on the notation and the definitions of Mathieu functions and their related properties, Fortran 90 subroutines to compute them are described and validated with some comparisons. A sample application is also provided.

rawabstract:
Software to compute angular and radial Mathieu functions is provided in the case that the parameter q is a complex variable and the independent variable x is real. After an introduction on the notation and the definitions of Mathieu functions and their related properties, Fortran 90 subroutines to compute them are described and validated with some comparisons. A sample application is also provided.

rawtitle:
{Algorithm 934}: {Fortran 90} subroutines to compute {Mathieu} functions for complex values of the parameter

entry:
@Article{Erricolo:2013:AFS,
  author =       "Danilo Erricolo and Giuseppe Carluccio",
  title =        "{Algorithm 934}: {Fortran 90} subroutines to compute
                 {Mathieu} functions for complex values of the
                 parameter",
  journal =      j-TOMS,
  volume =       "40",
  number =       "1",
  pages =        "8:1--8:19",
  month =        sep,
  year =         "2013",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2513109.2513117",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Sep 30 16:05:58 MDT 2013",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Software to compute angular and radial Mathieu
                 functions is provided in the case that the parameter q
                 is a complex variable and the independent variable x is
                 real. After an introduction on the notation and the
                 definitions of Mathieu functions and their related
                 properties, Fortran 90 subroutines to compute them are
                 described and validated with some comparisons. A sample
                 application is also provided.",
  acknowledgement = ack-nhfb,
  articleno =    "8",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: article
filename: elefunt.bib
label: Feng:2013:TFA
author: Lei Feng and Weiping Wang
title: Two families of approximations for the gamma function
journal: j-NUMER-ALGORITHMS
volume: 64
number: 3
pages: 403--416
month: nov
monthnumber: 11
year: 2013
CODEN: NUALEG
DOI: https://doi.org/10.1007/s11075-012-9671-x
ISSN: 1017-1398 (print), 1572-9265 (electronic) OR 10171398 (print), 15729265 (electronic)
ISSNL: 1017-1398 OR 10171398
bibdate: Mon Dec 2 18:18:12 MST 2013
bibtimestamp: 2013.12.02 18:18:12 MST
URL: http://link.springer.com/article/10.1007/s11075-012-9671-x
fjournal: Numerical Algorithms
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/11075
rawauthor: Lei Feng and Weiping Wang
rawtitle: Two families of approximations for the gamma function
bibsource:
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1017-1398&volume=64&issue=3; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib

entry:
@Article{Feng:2013:TFA,
  author =       "Lei Feng and Weiping Wang",
  title =        "Two families of approximations for the gamma
                 function",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "64",
  number =       "3",
  pages =        "403--416",
  month =        nov,
  year =         "2013",
  CODEN =        "NUALEG",
  DOI =          "https://doi.org/10.1007/s11075-012-9671-x",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Mon Dec 2 18:18:12 MST 2013",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1017-1398&volume=64&issue=3;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
  URL =          "http://link.springer.com/article/10.1007/s11075-012-9671-x",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
}


bibtype: article
filename: elefunt.bib
label: Fukushima:2013:PFC
author: Toshio Fukushima
title: Precise and fast computation of Jacobian elliptic functions by conditional duplication
journal: j-NUM-MATH
volume: 123
number: 4
pages: 585--605
month: apr
monthnumber: 4
year: 2013
CODEN: NUMMA7
DOI: https://doi.org/10.1007/s00211-012-0498-0
ISSN: 0029-599X (print), 0945-3245 (electronic) OR 0029599X (print), 09453245 (electronic)
ISSNL: 0029-599X OR 0029599X
bibdate: Sat Apr 27 13:30:29 MDT 2013
bibtimestamp: 2013.04.27 13:30:29 MDT
URL: http://link.springer.com/article/10.1007/s00211-012-0498-0
fjournal: Numerische Mathematik
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/211
rawauthor: Toshio Fukushima
rawtitle: Precise and fast computation of {Jacobian} elliptic functions by conditional duplication
bibsource:
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0029-599X&volume=123&issue=4; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/nummath2010.bib

entry:
@Article{Fukushima:2013:PFC,
  author =       "Toshio Fukushima",
  title =        "Precise and fast computation of {Jacobian} elliptic
                 functions by conditional duplication",
  journal =      j-NUM-MATH,
  volume =       "123",
  number =       "4",
  pages =        "585--605",
  month =        apr,
  year =         "2013",
  CODEN =        "NUMMA7",
  DOI =          "https://doi.org/10.1007/s00211-012-0498-0",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Sat Apr 27 13:30:29 MDT 2013",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0029-599X&volume=123&issue=4;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/nummath2010.bib",
  URL =          "http://link.springer.com/article/10.1007/s00211-012-0498-0",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}


bibtype: article
filename: elefunt.bib
label: Fukushima:2013:RCD
author: Toshio Fukushima
title: Recursive computation of derivatives of elliptic functions and of incomplete elliptic integrals
journal: j-APPL-MATH-COMP
volume: 221
pages: 21--31
day: 15
month: sep
monthnumber: 9
year: 2013
CODEN: AMHCBQ
ISSN: 0096-3003 (print), 1873-5649 (electronic) OR 00963003 (print), 18735649 (electronic)
ISSNL: 0096-3003 OR 00963003
bibdate: Mon Dec 2 12:34:28 MST 2013
bibtimestamp: 2013.12.02 12:34:28 MST
URL: http://www.sciencedirect.com/science/article/pii/S0096300313006152
fjournal: Applied Mathematics and Computation
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00963003
rawauthor: Toshio Fukushima
rawtitle: Recursive computation of derivatives of elliptic functions and of incomplete elliptic integrals
entry:
@Article{Fukushima:2013:RCD,
  author =       "Toshio Fukushima",
  title =        "Recursive computation of derivatives of elliptic
                 functions and of incomplete elliptic integrals",
  journal =      j-APPL-MATH-COMP,
  volume =       "221",
  number =       "??",
  pages =        "21--31",
  day =          "15",
  month =        sep,
  year =         "2013",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Mon Dec 2 12:34:28 MST 2013",
  bibsource =    "http://www.sciencedirect.com/science/journal/00963003;
                 https://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0096300313006152",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
}


bibtype: article
filename: elefunt.bib
label: Gonzalez-Morales:2013:NII
author: M. J. Gonzalez-Morales and R. Mahillo-Isla and C. Dehesa-Martinez
title: A new integral identity involving the elliptic integral $ E(m) $
journal: j-APPL-MATH-COMP
volume: 221
pages: 568--570
day: 15
month: sep
monthnumber: 9
year: 2013
CODEN: AMHCBQ
ISSN: 0096-3003 (print), 1873-5649 (electronic) OR 00963003 (print), 18735649 (electronic)
ISSNL: 0096-3003 OR 00963003
bibdate: Mon Dec 2 12:34:28 MST 2013
bibtimestamp: 2013.12.02 12:34:28 MST
URL: http://www.sciencedirect.com/science/article/pii/S0096300313007303
fjournal: Applied Mathematics and Computation
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00963003/
rawauthor: M. J. Gonz{\'a}lez-Morales and R. Mahillo-Isla and C. Dehesa-Mart{\'\i}nez
rawtitle: A new integral identity involving the elliptic integral {$ E(m) $}
bibsource:
https://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Gonzalez-Morales:2013:NII,
  author =       "M. J. Gonz{\'a}lez-Morales and R. Mahillo-Isla and C.
                 Dehesa-Mart{\'\i}nez",
  title =        "A new integral identity involving the elliptic
                 integral {$ E(m) $}",
  journal =      j-APPL-MATH-COMP,
  volume =       "221",
  number =       "??",
  pages =        "568--570",
  day =          "15",
  month =        sep,
  year =         "2013",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Mon Dec 2 12:34:28 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0096300313007303",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003/",
}


bibtype: article
filename: elefunt.bib
label: Hale:2013:FAC
author: Nicholas Hale and Alex Townsend
title: Fast and Accurate Computation of Gauss--Legendre and Gauss--Jacobi Quadrature Nodes and Weights
journal: j-SIAM-J-SCI-COMP
volume: 35
number: 2
pages: A652--A674
year: 2013
CODEN: SJOCE3
DOI: https://doi.org/10.1137/120889873
ISSN: 1064-8275 (print), 1095-7197 (electronic) OR 10648275 (print), 10957197 (electronic)
ISSNL: 1064-8275 OR 10648275
bibdate: Fri Jul 19 07:43:46 MDT 2013
bibtimestamp: 2013.07.19 07:43:46 MDT
fjournal: SIAM Journal on Scientific Computing
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sisc
onlinedate: January 2013
rawauthor: Nicholas Hale and Alex Townsend
rawtitle: Fast and Accurate Computation of {Gauss--Legendre} and {Gauss--Jacobi} Quadrature Nodes and Weights
bibsource:
http://epubs.siam.org/sam-bin/dbq/toc/SISC/35/2; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib

entry:
@Article{Hale:2013:FAC,
  author =       "Nicholas Hale and Alex Townsend",
  title =        "Fast and Accurate Computation of {Gauss--Legendre} and
                 {Gauss--Jacobi} Quadrature Nodes and Weights",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "35",
  number =       "2",
  pages =        "A652--A674",
  month =        "????",
  year =         "2013",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/120889873",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  bibdate =      "Fri Jul 19 07:43:46 MDT 2013",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SISC/35/2;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
  onlinedate =   "January 2013",
}


bibtype: article
filename: elefunt.bib
label: Huang:2013:NNE
author: Zhi-Wei Huang and Jueping Liu
title: NumExp: Numerical epsilon expansion of hypergeometric functions
journal: j-COMP-PHYS-COMM
volume: 184
number: 8
pages: 1973--1980
month: aug
monthnumber: 8
year: 2013
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/j.cpc.2013.03.016
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Wed May 15 07:02:08 MDT 2013
bibtimestamp: 2013.05.15 07:02:08 MDT
URL: http://www.sciencedirect.com/science/article/pii/S0010465513001136
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: Zhi-Wei Huang and Jueping Liu
rawtitle: {NumExp}: Numerical epsilon expansion of hypergeometric functions
entry:
@Article{Huang:2013:NNE,
  author =       "Zhi-Wei Huang and Jueping Liu",
  title =        "{NumExp}: Numerical epsilon expansion of
                 hypergeometric functions",
  journal =      j-COMP-PHYS-COMM,
  volume =       "184",
  number =       "8",
  pages =        "1973--1980",
  month =        aug,
  year =         "2013",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/j.cpc.2013.03.016",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Wed May 15 07:02:08 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465513001136",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}


bibtype: article
filename: elefunt.bib
label: Jablonski:2013:IAC
author: A. Jablonski
title: Improved algorithm for calculating the Chandrasekhar function
journal: j-COMP-PHYS-COMM
volume: 184
number: 2
pages: 440--442
month: feb
monthnumber: 2
year: 2013
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/j.cpc.2012.08.020
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Fri Nov 2 11:55:56 MDT 2012
bibtimestamp: 2012.11.02 11:55:56 MDT
URL: http://www.sciencedirect.com/science/article/pii/S001046551200286X
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: A. Jablonski
rawtitle: Improved algorithm for calculating the {Chandrasekhar} function
entry:
@Article{Jablonski:2013:IAC,
  author =       "A. Jablonski",
  title =        "Improved algorithm for calculating the {Chandrasekhar}
                 function",
  journal =      j-COMP-PHYS-COMM,
  volume =       "184",
  number =       "2",
  pages =        "440--442",
  month =        feb,
  year =         "2013",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/j.cpc.2012.08.020",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Fri Nov 2 11:55:56 MDT 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S001046551200286X",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}


bibtype: inproceedings
filename: elefunt.bib
label: Jiang:2013:AFE
author: Hao Jiang and Stef Graillat and Roberto Barrio
title: Accurate and Fast Evaluation of Elementary Symmetric Functions
crossref: IEEE:2013:PIS
pages: 183--190
year: 2013
DOI: https://doi.org/10.1109/ARITH.2013.18
ISSN: 1063-6889 OR 10636889
bibdate: Sat Aug 1 09:38:32 2015
bibtimestamp: 2015.08.01 09:38:32 ???
acknowledgement: ack-nhfb
rawauthor: Hao Jiang and Stef Graillat and Roberto Barrio
rawtitle: Accurate and Fast Evaluation of Elementary Symmetric Functions
keywords:
Accuracy; accurate algorithm; Algorithm design and analysis; ARITH-21; compensated algorithm; double-double library; elementary symmetric functions; error-free transformation; error-free transformations; floating point arithmetic; floating-point arithmetic; forward roundoff error bound; Libraries; mathematics computing; MATLAB poly function; Polynomials; psychological measurement; Rasch model; roundoff error; Roundoff errors; running error bound; shaper bound; summation algorithm; Vectors

entry:
@InProceedings{Jiang:2013:AFE,
  author =       "Hao Jiang and Stef Graillat and Roberto Barrio",
  title =        "Accurate and Fast Evaluation of Elementary Symmetric
                 Functions",
  crossref =     "IEEE:2013:PIS",
  pages =        "183--190",
  year =         "2013",
  DOI =          "https://doi.org/10.1109/ARITH.2013.18",
  ISSN =         "1063-6889",
  bibdate =      "Sat Aug 1 09:38:32 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Accuracy; accurate algorithm; Algorithm design and
                 analysis; ARITH-21; compensated algorithm;
                 double-double library; elementary symmetric functions;
                 error-free transformation; error-free transformations;
                 floating point arithmetic; floating-point arithmetic;
                 forward roundoff error bound; Libraries; mathematics
                 computing; MATLAB poly function; Polynomials;
                 psychological measurement; Rasch model; roundoff error;
                 Roundoff errors; running error bound; shaper bound;
                 summation algorithm; Vectors",
}


bibtype: article
filename: elefunt.bib
label: Lopez:2013:NSE
author: Jose L. Lopez and Nico M. Temme
title: New series expansions of the Gauss hypergeometric function
journal: j-ADV-COMPUT-MATH
volume: 39
number: 2
pages: 349--365
month: aug
monthnumber: 8
year: 2013
CODEN: ACMHEX
DOI: https://doi.org/10.1007/s10444-012-9283-y
ISSN: 1019-7168 (print), 1572-9044 (electronic) OR 10197168 (print), 15729044 (electronic)
ISSNL: 1019-7168 OR 10197168
MRclass: 33C05 (33F05 41A58 65D20)
MRnumber: 3082518
MRreviewer: Jochen Denzler
bibdate: Sat Feb 3 18:23:06 MST 2018
bibtimestamp: 2018.02.03 18:23:06 MST
URL: http://link.springer.com/article/10.1007/s10444-012-9283-y
fjournal: Advances in Computational Mathematics
keywords: Gauss hypergeometric function $_2F_1(a,b,c; z)$
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10444
rawauthor: Jos{\'e} L. L{\'o}pez and Nico M. Temme
rawtitle: New series expansions of the {Gauss} hypergeometric function
bibsource:
https://www.math.utah.edu/pub/tex/bib/advcomputmath.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

remark:
Improvement on cite Buhring:1987:ACH,Buhring:1987:BUA and cite [ 2.3]Gil:2007:NMS by removal of points excluded from the domain of convergence.

entry:
@Article{Lopez:2013:NSE,
  author =       "Jos{\'e} L. L{\'o}pez and Nico M. Temme",
  title =        "New series expansions of the {Gauss} hypergeometric
                 function",
  journal =      j-ADV-COMPUT-MATH,
  volume =       "39",
  number =       "2",
  pages =        "349--365",
  month =        aug,
  year =         "2013",
  CODEN =        "ACMHEX",
  DOI =          "https://doi.org/10.1007/s10444-012-9283-y",
  ISSN =         "1019-7168 (print), 1572-9044 (electronic)",
  ISSN-L =       "1019-7168",
  MRclass =      "33C05 (33F05 41A58 65D20)",
  MRnumber =     "3082518",
  MRreviewer =   "Jochen Denzler",
  bibdate =      "Sat Feb 3 18:23:06 MST 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/advcomputmath.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://link.springer.com/article/10.1007/s10444-012-9283-y",
  acknowledgement = ack-nhfb,
  fjournal =     "Advances in Computational Mathematics",
  journal-URL =  "http://link.springer.com/journal/10444",
  keywords =     "Gauss hypergeometric function $_2F_1(a,b,c; z)$",
  remark =       "Improvement on
                 \cite{Buhring:1987:ACH,Buhring:1987:BUA} and \cite[\S
                 2.3]{Gil:2007:NMS} by removal of points excluded from
                 the domain of convergence.",
}


bibtype: article
filename: elefunt.bib
label: Low:2013:MET
author: Joshua Yung Lih Low and Ching Chuen Jong
title: A Memory-Efficient Tables-and-Additions Method for Accurate Computation of Elementary Functions
journal: j-IEEE-TRANS-COMPUT
volume: 62
number: 5
pages: 858--872
month: may
monthnumber: 5
year: 2013
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.2012.43
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Apr 30 12:26:22 2013
bibtimestamp: 2013.04.30 12:26:22 ???
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Joshua Yung Lih Low and Ching Chuen Jong
rawtitle: A Memory-Efficient Tables-and-Additions Method for Accurate Computation of Elementary Functions
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib

entry:
@Article{Low:2013:MET,
  author =       "Joshua Yung Lih Low and Ching Chuen Jong",
  title =        "A Memory-Efficient Tables-and-Additions Method for
                 Accurate Computation of Elementary Functions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "62",
  number =       "5",
  pages =        "858--872",
  month =        may,
  year =         "2013",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2012.43",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Apr 30 12:26:22 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: elefunt.bib
label: Mastin:2013:LQB
author: Andrew Mastin and Patrick Jaillet
title: Log-quadratic bounds for the Gaussian $Q$-function
journal: arxiv.org
pages: ??--??
day: 9
month: apr
monthnumber: 4
year: 2013
bibdate: Sat Dec 16 17:09:03 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.12.16 17:09:03 ???
URL: http://arxiv.org/abs/1304.2488
acknowledgement: ack-nhfb
rawauthor: Andrew Mastin and Patrick Jaillet
rawtitle: Log-quadratic bounds for the {Gaussian} {$Q$}-function
entry:
@Article{Mastin:2013:LQB,
  author =       "Andrew Mastin and Patrick Jaillet",
  title =        "Log-quadratic bounds for the {Gaussian}
                 {$Q$}-function",
  journal =      "arxiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "9",
  month =        apr,
  year =         "2013",
  bibdate =      "Sat Dec 16 17:09:03 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://arxiv.org/abs/1304.2488",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Neta:2013:FHL
author: Beny Neta and Melvin Scott
title: On a family of Halley-like methods to find simple roots of nonlinear equations
journal: j-APPL-MATH-COMP
volume: 219
number: 15
pages: 7940--7944
day: 1
month: apr
monthnumber: 4
year: 2013
CODEN: AMHCBQ
DOI: https://doi.org/10.1016/j.amc.2013.02.035
ISSN: 0096-3003 (print), 1873-5649 (electronic) OR 00963003 (print), 18735649 (electronic)
ISSNL: 0096-3003 OR 00963003
bibdate: Mon May 6 18:04:12 MDT 2013
bibtimestamp: 2013.05.06 18:04:12 MDT
URL: http://www.sciencedirect.com/science/article/pii/S0096300313001574
fjournal: Applied Mathematics and Computation
keywords: basin of attraction; Euler--Chebyshev method; Halley method; nonlinear equations; simple roots
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00963003/
rawauthor: Beny Neta and Melvin Scott
rawtitle: On a family of {Halley}-like methods to find simple roots of nonlinear equations
bibsource:
https://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Neta:2013:FHL,
  author =       "Beny Neta and Melvin Scott",
  title =        "On a family of {Halley}-like methods to find simple
                 roots of nonlinear equations",
  journal =      j-APPL-MATH-COMP,
  volume =       "219",
  number =       "15",
  pages =        "7940--7944",
  day =          "1",
  month =        apr,
  year =         "2013",
  CODEN =        "AMHCBQ",
  DOI =          "https://doi.org/10.1016/j.amc.2013.02.035",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Mon May 6 18:04:12 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0096300313001574",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003/",
  keywords =     "basin of attraction; Euler--Chebyshev method; Halley
                 method; nonlinear equations; simple roots",
}


bibtype: book
filename: elefunt.bib
label: Osipov:2013:PSW
author: Andrei Osipov
title: Prolate Spheroidal Wave Functions of Order Zero: Mathematical Tools for Bandlimited Approximation
publisher: pub-SV
address: pub-SV:adr
year: 2013
ISBN: 1-4614-8258-5 OR 1461482585
ISBN13: 978-1-4614-8258-1 OR 9781461482581
bibdate: Sat Apr 1 14:32:29 MDT 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2017.04.01 14:32:29 MDT
acknowledgement: ack-nhfb
rawauthor: Andrei Osipov
rawtitle: Prolate Spheroidal Wave Functions of Order Zero: Mathematical Tools for Bandlimited Approximation
URL:
http://www.loc.gov/catdir/enhancements/fy1315/2013945079-b.html; http://www.loc.gov/catdir/enhancements/fy1315/2013945079-d.html; http://www.loc.gov/catdir/enhancements/fy1315/2013945079-t.html

TOC:
Introduction Mathematical and Numerical Preliminaries Overview Analysis of the Differential Operator Analysis of the Integral Operator Rational Approximations of PSWFs Miscellaneous Properties of PSWFs Asymptotic Analysis of PSWFs Quadrature Rules and Interpolation via PSWFs Numerical Algorithms

rawTOC:
Introduction \\ Mathematical and Numerical Preliminaries \\ Overview \\ Analysis of the Differential Operator \\ Analysis of the Integral Operator \\ Rational Approximations of PSWFs \\ Miscellaneous Properties of PSWFs \\ Asymptotic Analysis of PSWFs \\ Quadrature Rules and Interpolation via PSWFs \\ Numerical Algorithms

entry:
@Book{Osipov:2013:PSW,
  author =       "Andrei Osipov",
  title =        "Prolate Spheroidal Wave Functions of Order Zero:
                 Mathematical Tools for Bandlimited Approximation",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "????",
  year =         "2013",
  ISBN =         "1-4614-8258-5",
  ISBN-13 =      "978-1-4614-8258-1",
  LCCN =         "????",
  bibdate =      "Sat Apr 1 14:32:29 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://www.loc.gov/catdir/enhancements/fy1315/2013945079-b.html;
                 http://www.loc.gov/catdir/enhancements/fy1315/2013945079-d.html;
                 http://www.loc.gov/catdir/enhancements/fy1315/2013945079-t.html",
  acknowledgement = ack-nhfb,
  tableofcontents = "Introduction \\
                 Mathematical and Numerical Preliminaries \\
                 Overview \\
                 Analysis of the Differential Operator \\
                 Analysis of the Integral Operator \\
                 Rational Approximations of PSWFs \\
                 Miscellaneous Properties of PSWFs \\
                 Asymptotic Analysis of PSWFs \\
                 Quadrature Rules and Interpolation via PSWFs \\
                 Numerical Algorithms",
}


bibtype: article
filename: elefunt.bib
label: Russinoff:2013:CFV
author: David M. Russinoff
title: Computation and Formal Verification of SRT Quotient and Square Root Digit Selection Tables
journal: j-IEEE-TRANS-COMPUT
volume: 62
number: 5
pages: 900--913
month: may
monthnumber: 5
year: 2013
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.2012.40
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Apr 30 12:26:22 2013
bibtimestamp: 2013.04.30 12:26:22 ???
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: David M. Russinoff
rawtitle: Computation and Formal Verification of {SRT} Quotient and Square Root Digit Selection Tables
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib

entry:
@Article{Russinoff:2013:CFV,
  author =       "David M. Russinoff",
  title =        "Computation and Formal Verification of {SRT} Quotient
                 and Square Root Digit Selection Tables",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "62",
  number =       "5",
  pages =        "900--913",
  month =        may,
  year =         "2013",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2012.40",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Apr 30 12:26:22 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: elefunt.bib
label: Szmytkowski:2013:EBT
author: Radoslaw Szmytkowski
journal: j-MATH-COMPUT
volume: 82
number: 283
pages: 1709--1710
year: 2013
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Apr 30 16:18:02 MDT 2013
bibtimestamp: 2013.04.30 16:18:02 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Rados{\l}aw Szmytkowski
title:
Erratum to booktitle Formulas and Theorems for the Special Functions of Mathematical Physics by W. Magnus, F. Oberhettinger, R. P. Soni

bibsource:
http://www.ams.org/mcom/2013-82-283; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp2010.bib

URL:
http://www.ams.org/journals/mcom/2013-82-283/S0025-5718-2013-02671-3; http://www.ams.org/journals/mcom/2013-82-283/S0025-5718-2013-02671-3/S0025-5718-2013-02671-3.pdf

rawtitle:
Erratum to {{\booktitle{Formulas and Theorems for the Special Functions of Mathematical Physics}} by W. Magnus, F. Oberhettinger, R. P. Soni}

entry:
@Article{Szmytkowski:2013:EBT,
  author =       "Rados{\l}aw Szmytkowski",
  title =        "Erratum to {{\booktitle{Formulas and Theorems for the
                 Special Functions of Mathematical Physics}} by W.
                 Magnus, F. Oberhettinger, R. P. Soni}",
  journal =      j-MATH-COMPUT,
  volume =       "82",
  number =       "283",
  pages =        "1709--1710",
  month =        "????",
  year =         "2013",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Apr 30 16:18:02 MDT 2013",
  bibsource =    "http://www.ams.org/mcom/2013-82-283;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp2010.bib",
  URL =          "http://www.ams.org/journals/mcom/2013-82-283/S0025-5718-2013-02671-3;
                 http://www.ams.org/journals/mcom/2013-82-283/S0025-5718-2013-02671-3/S0025-5718-2013-02671-3.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Thompson:2013:AIG
author: Ian Thompson
title: Algorithm 926: Incomplete Gamma Functions with Negative Arguments
journal: j-TOMS
volume: 39
number: 2
pages: 14:1--14:9
month: feb
monthnumber: 2
year: 2013
CODEN: ACMSCU
DOI: https://doi.org/10.1145/2427023.2427031
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Wed Feb 20 16:46:13 MST 2013
bibtimestamp: 2013.02.20 16:46:13 MST
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
articleno: 14
journalURL: https://dl.acm.org/loi/toms
rawauthor: Ian Thompson
rawtitle: {Algorithm 926}: Incomplete {Gamma} Functions with Negative Arguments
abstract:
An algorithm for accurately computing the lower incomplete gamma function $ gamma (a, t) $ in the case where $ a = n + 1 / 2 $, $ n in Z $ and $ t < 0 $ is described. Series expansions and analytic continuation are employed to compute the function for certain critical values of $n$, and these results are used to initiate stable recurrence. The algorithm has been implemented in Fortran 2003, with precomputations carried out in Maple.

rawabstract:
An algorithm for accurately computing the lower incomplete gamma function $ \gamma (a, t) $ in the case where $ a = n + 1 / 2 $, $ n \in Z $ and $ t < 0 $ is described. Series expansions and analytic continuation are employed to compute the function for certain critical values of $n$, and these results are used to initiate stable recurrence. The algorithm has been implemented in Fortran 2003, with precomputations carried out in Maple.

entry:
@Article{Thompson:2013:AIG,
  author =       "Ian Thompson",
  title =        "{Algorithm 926}: Incomplete {Gamma} Functions with
                 Negative Arguments",
  journal =      j-TOMS,
  volume =       "39",
  number =       "2",
  pages =        "14:1--14:9",
  month =        feb,
  year =         "2013",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2427023.2427031",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 20 16:46:13 MST 2013",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "An algorithm for accurately computing the lower
                 incomplete gamma function $ \gamma (a, t) $ in the case
                 where $ a = n + 1 / 2 $, $ n \in Z $ and $ t < 0 $ is
                 described. Series expansions and analytic continuation
                 are employed to compute the function for certain
                 critical values of $n$, and these results are used to
                 initiate stable recurrence. The algorithm has been
                 implemented in Fortran 2003, with precomputations
                 carried out in Maple.",
  acknowledgement = ack-nhfb,
  articleno =    "14",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


