# bibtab

bibtype: techreport
filename: elefunt.bib
label: Fox:1977:PMS
author: P. A. Fox and A. D. Hall and N. L. Schryer
title: The PORT Mathematical Subroutine Library
type: Computing Science Technical Report
number: 47
institution: inst-ATT-BELL
address: inst-ATT-BELL:adr
pages: ii + 50
day: 22
month: mar
monthnumber: 3
year: 1977
bibdate: Fri Sep 01 09:08:27 2023
bibtimestamp: 2023.09.01 09:08:27 ???
URL: http://history.siam.org/%5C/sup/Fox_bell_subroutine.pdf
remark: May 1977 revision of version of September 1976.
acknowledgement: ack-nhfb
rawauthor: P. A. Fox and A. D. Hall and N. L. Schryer
rawtitle: The {PORT} Mathematical Subroutine Library
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fortran1.bib; https://www.math.utah.edu/pub/tex/bib/unix.bib

abstract:
The development at Bell Laboratories of PORT, a library of portable Fortran programs for numerical computation, is discussed.par Portability is achieved by careful language specification, together with the key technique of specifying computer classes by means of pre-defined machine constants.par The library is built around an automatic error-handling facility and a dynamic storage allocation scheme, both of which are implemented portably. These, together with the modular structure of the library, lead to simplified calling sequences and ease of use.

TOC:
Part 1: Description Part 2: Utility program listings: Machine constants Error handling Stack allocation

rawabstract:
The development at Bell Laboratories of PORT, a library of portable Fortran programs for numerical computation, is discussed.\par Portability is achieved by careful language specification, together with the key technique of specifying computer classes by means of pre-defined machine constants.\par The library is built around an automatic error-handling facility and a dynamic storage allocation scheme, both of which are implemented portably. These, together with the modular structure of the library, lead to simplified calling sequences and ease of use.

rawTOC:
Part 1: Description \\ Part 2: Utility program listings: \\ Machine constants \\ Error handling \\ Stack allocation

entry:
@TechReport{Fox:1977:PMS,
  author =       "P. A. Fox and A. D. Hall and N. L. Schryer",
  title =        "The {PORT} Mathematical Subroutine Library",
  type =         "Computing Science Technical Report",
  number =       "47",
  institution =  inst-ATT-BELL,
  address =      inst-ATT-BELL:adr,
  pages =        "ii + 50",
  day =          "22",
  month =        mar,
  year =         "1977",
  bibdate =      "Fri Sep 01 09:08:27 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fortran1.bib;
                 https://www.math.utah.edu/pub/tex/bib/unix.bib",
  URL =          "http://history.siam.org/%5C/sup/Fox_bell_subroutine.pdf",
  abstract =     "The development at Bell Laboratories of PORT, a
                 library of portable Fortran programs for numerical
                 computation, is discussed.\par

                 Portability is achieved by careful language
                 specification, together with the key technique of
                 specifying computer classes by means of pre-defined
                 machine constants.\par

                 The library is built around an automatic error-handling
                 facility and a dynamic storage allocation scheme, both
                 of which are implemented portably. These, together with
                 the modular structure of the library, lead to
                 simplified calling sequences and ease of use.",
  acknowledgement = ack-nhfb,
  remark =       "May 1977 revision of version of September 1976.",
  tableofcontents = "Part 1: Description \\
                 Part 2: Utility program listings: \\
                 Machine constants \\
                 Error handling \\
                 Stack allocation",
}


bibtype: inproceedings
filename: elefunt.bib
label: Fullerton:1977:PSF
author: L. W. Fullerton
title: Portable Special Function Routines
crossref: Cowell:1977:PMS
pages: 452--483
year: 1977
bibdate: Sat Oct 30 06:40:00 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.30 06:40:00 ???
acknowledgement: ack-nhfb
rawauthor: L. W. Fullerton
rawtitle: Portable Special Function Routines
entry:
@InProceedings{Fullerton:1977:PSF,
  author =       "L. W. Fullerton",
  title =        "Portable Special Function Routines",
  crossref =     "Cowell:1977:PMS",
  pages =        "452--483",
  year =         "1977",
  bibdate =      "Sat Oct 30 06:40:00 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
}


bibtype: article
filename: elefunt.bib
label: Gautschi:1977:ACC
author: Walter Gautschi
title: Anomalous convergence of a continued fraction for ratios of Kummer functions
journal: j-MATH-COMPUT
volume: 31
number: 140
pages: 994--999
month: oct
monthnumber: 10
year: 1977
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
classcodes: C1120 (Mathematical analysis); C4170 (Differential equations)
corpsource: Dept. of Computer Sci., Purdue Univ., Lafayette, IN, USA
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: Walter Gautschi
rawtitle: Anomalous convergence of a continued fraction for ratios of {Kummer} functions
keywords:
apparent; Bessel functions; continued fraction; convergence; differential equations; gamma functions; Kummer functions; wrong limit

entry:
@Article{Gautschi:1977:ACC,
  author =       "Walter Gautschi",
  title =        "Anomalous convergence of a continued fraction for
                 ratios of {Kummer} functions",
  journal =      j-MATH-COMPUT,
  volume =       "31",
  number =       "140",
  pages =        "994--999",
  month =        oct,
  year =         "1977",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "C1120 (Mathematical analysis); C4170 (Differential
                 equations)",
  corpsource =   "Dept. of Computer Sci., Purdue Univ., Lafayette, IN,
                 USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "apparent; Bessel functions; continued fraction;
                 convergence; differential equations; gamma functions;
                 Kummer functions; wrong limit",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Gautschi:1977:ERI
author: Walter Gautschi
title: Evaluation of Repeated Integrals of the Coerror Function
journal: j-TOMS
volume: 3
number: 3
pages: 240--252
month: sep
monthnumber: 9
year: 1977
CODEN: ACMSCU
DOI: https://doi.org/10.1145/355744.355748
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Sat Aug 27 22:26:34 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.08.27 22:26:34 ???
fjournal: ACM Transactions on Mathematical Software (TOMS)
remark: Fullerton: An arbitrary-accuracy method for evaluating $ i^n erfc (x) $ is given.
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Walter Gautschi
rawtitle: Evaluation of Repeated Integrals of the Coerror Function
entry:
@Article{Gautschi:1977:ERI,
  author =       "Walter Gautschi",
  title =        "Evaluation of Repeated Integrals of the Coerror
                 Function",
  journal =      j-TOMS,
  volume =       "3",
  number =       "3",
  pages =        "240--252",
  month =        sep,
  year =         "1977",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355744.355748",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 22:26:34 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  remark =       "Fullerton: An arbitrary-accuracy method for evaluating
                 $ i^n \erfc (x) $ is given.",
}


bibtype: article
filename: elefunt.bib
label: Harris:1977:CAT
author: F. E. Harris
journal: j-J-MATH-PHYS
volume: 18
number: 12
pages: 2377--2381
month: dec
monthnumber: 12
year: 1977
CODEN: JMAPAQ
ISSNL: 0022-2488 OR 00222488
bibdate: Fri Jan 2 14:59:17 MST 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1998.01.02 14:59:17 MST
fjournal: Journal of Mathematical Physics
acknowledgement: ack-nhfb
corpsource: Dept. of Chem., Univ. of Hawaii, Honolulu, HI, USA
journalURL: http://jmp.aip.org/
treatment: T Theoretical or Mathematical
rawauthor: F. E. Harris
title:
Convergence acceleration technique for lattice sums arising in electronic-structure studies of crystalline solids

keywords:
convergence acceleration; convergence of numerical methods; crystalline solids; electronic structure; Laplace transform; Laplace transforms; lattice energy; lattice sums; Poisson's summation formula

rawtitle:
Convergence acceleration technique for lattice sums arising in electronic-structure studies of crystalline solids

entry:
@Article{Harris:1977:CAT,
  author =       "F. E. Harris",
  title =        "Convergence acceleration technique for lattice sums
                 arising in electronic-structure studies of crystalline
                 solids",
  journal =      j-J-MATH-PHYS,
  volume =       "18",
  number =       "12",
  pages =        "2377--2381",
  month =        dec,
  year =         "1977",
  CODEN =        "JMAPAQ",
  ISSN =         "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
  ISSN-L =       "0022-2488",
  bibdate =      "Fri Jan 2 14:59:17 MST 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  classification = "A0260 (Numerical approximation and analysis); A6150L
                 (Crystal binding)",
  corpsource =   "Dept. of Chem., Univ. of Hawaii, Honolulu, HI, USA",
  fjournal =     "Journal of Mathematical Physics",
  journal-URL =  "http://jmp.aip.org/",
  keywords =     "convergence acceleration; convergence of numerical
                 methods; crystalline solids; electronic structure;
                 Laplace transform; Laplace transforms; lattice energy;
                 lattice sums; Poisson's summation formula",
  pubcountry =   "USA",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: book
filename: elefunt.bib
label: Henrici:1977:ART
author: Peter Henrici
publisher: Oldenbourg
address: Munchen, West Germany
pages: 280
year: 1977
ISBN: 0-471-02938-6 OR 0471029386
ISBN13: 978-0-471-02938-0 OR 9780471029380
bibdate: Mon Jan 28 08:25:06 MST 2019
bibtimestamp: 2019.01.28 08:25:06 MST
language: German
subject: Numerische Mathematik; Programmierung <EDV>; Kleinrechner
acknowledgement: ack-nhfb
authordates: 1923--1987
rawauthor: Peter Henrici
title:
Analytische Rechenverfahren fur den Taschenrechner HP-25. (German) [Analytical Calculations for the HP-25 Calculator]

bibsource:
fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/bibnet/authors/h/henrici-peter.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

TOC:
Einleitung / 9 Teil I: Zahlentheorie / 13 Primfaktorzerlegung / 14 Euklidscher Algorithmus / 18 Rationale Binomialkoeffizienten / 22 Kettenbruchdarstellungen reeller Zahlen / 28 Genaue Kettenbruchdarstellungen von quadratischen Irrationalitaten / 33 Teil II: Iteration / 39 Iteration / 40 Iteration mit Aitken-Beschleunigung / 45 Aitken--Steffensen-Iteration / 50 Newton-Iteration fur Wurzeln komplexer Zahlen / 55 Teil III: Polynome / 61 Der Horner-Algorithmus 6 / 2 Das Newton-Verfahren bei Polynomen / 66 Bernoulli-Verfahren: Eine reelle dominante Nullstelle / 71 Bernoulli-Verfahren: Zwei konjugiert komplexe dominante Nullstellen / 76 Der Quotienten--Differenzen-Algorithmus / 82 Der Routh-Algorithmus / 87 Der Schur--Cohn-Algorithmus I / 92 Der Schur--Cohn-Algorithmus II / 97 Teil IV: Potenzreihen / 101 Reziproke Potenzreihe / 102 Potenz einer Potenzreihe / 111 Exponentiation einer Potenzreihe / 118 Teil V: Integration / 123 Numerische Integration mit Schrittverfeinerung / 124 Der Romberg-Algorithmus / 129 Die Planasche Summationsformel / 136 Eine Differentialgleichung erster Ordnung: Trapezregel / 143 Autonome Differentialgleichung zweiter Ordnung ohne erste Ableitung / 150 Lineare Differentialgleichung zweiter Ordnung / 155 Teil VI: Spezielle Konstanten und Funktionen / 161 Log-Arcsinus-Algorithmus / 162 Die Gamma-Funktion / 167 Unvollstandige Gamma-Funktion / 174 Die Fehlerfunktion / 181 Vollstandige elliptische Integrale / 187 Besselfunktionen ganzzahliger Ordnung / 191 Besselfunktionen beliebiger Ordnung / 196 Besselfunktionen: Asymptotische Reihe / 201 Die Riemannsche Zetafunktion auf der kritischen Geraden / 207 Stichwortverzeichnis / 213

rawtitle:
{Analytische Rechenverfahren f{\"u}r den Taschenrechner HP-25}. ({German}) [{Analytical} Calculations for the {HP-25} Calculator]

rawTOC:
Einleitung / 9 \\ Teil I: Zahlentheorie / 13 \\ Primfaktorzerlegung / 14 \\ Euklidscher Algorithmus / 18 \\ Rationale Binomialkoeffizienten / 22 \\ Kettenbruchdarstellungen reeller Zahlen / 28 \\ Genaue Kettenbruchdarstellungen von quadratischen Irrationalit{\"a}ten / 33 \\ Teil II: Iteration / 39 \\ Iteration / 40 \\ Iteration mit Aitken-Beschleunigung / 45 \\ Aitken--Steffensen-Iteration / 50 \\ Newton-Iteration f{\"u}r Wurzeln komplexer Zahlen / 55 \\ Teil III: Polynome / 61 \\ Der Horner-Algorithmus 6 / 2 \\ Das Newton-Verfahren bei Polynomen / 66 \\ Bernoulli-Verfahren: Eine reelle dominante Nullstelle / 71 \\ Bernoulli-Verfahren: Zwei konjugiert komplexe dominante Nullstellen / 76 \\ Der Quotienten--Differenzen-Algorithmus / 82 \\ Der Routh-Algorithmus / 87 \\ Der Schur--Cohn-Algorithmus I / 92 \\ Der Schur--Cohn-Algorithmus II / 97 \\ Teil IV: Potenzreihen / 101 \\ Reziproke Potenzreihe / 102 \\ Potenz einer Potenzreihe / 111 \\ Exponentiation einer Potenzreihe / 118 \\ Teil V: Integration / 123 \\ Numerische Integration mit Schrittverfeinerung / 124 \\ Der Romberg-Algorithmus / 129 \\ Die Planasche Summationsformel / 136 \\ Eine Differentialgleichung erster Ordnung: Trapezregel / 143 \\ Autonome Differentialgleichung zweiter Ordnung ohne erste Ableitung / 150 \\ Lineare Differentialgleichung zweiter Ordnung / 155 \\ Teil VI: Spezielle Konstanten und Funktionen / 161 \\ Log-Arcsinus-Algorithmus / 162 \\ Die Gamma-Funktion / 167 \\ Unvollst{\"a}ndige Gamma-Funktion / 174 \\ Die Fehlerfunktion / 181 \\ Vollst{\"a}ndige elliptische Integrale / 187 \\ Besselfunktionen ganzzahliger Ordnung / 191 \\ Besselfunktionen beliebiger Ordnung / 196 \\ Besselfunktionen: Asymptotische Reihe / 201 \\ Die Riemannsche Zetafunktion auf der kritischen Geraden / 207 \\ Stichwortverzeichnis / 213

entry:
@Book{Henrici:1977:ART,
  author =       "Peter Henrici",
  title =        "{Analytische Rechenverfahren f{\"u}r den
                 Taschenrechner HP-25}. ({German}) [{Analytical}
                 Calculations for the {HP-25} Calculator]",
  publisher =    "Oldenbourg",
  address =      "M{\"u}nchen, West Germany",
  pages =        "280",
  year =         "1977",
  ISBN =         "0-471-02938-6",
  ISBN-13 =      "978-0-471-02938-0",
  LCCN =         "????",
  bibdate =      "Mon Jan 28 08:25:06 MST 2019",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/bibnet/authors/h/henrici-peter.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  author-dates = "1923--1987",
  language =     "German",
  subject =      "Numerische Mathematik; Programmierung <EDV>;
                 Kleinrechner",
  tableofcontents = "Einleitung / 9 \\
                 Teil I: Zahlentheorie / 13 \\
                 Primfaktorzerlegung / 14 \\
                 Euklidscher Algorithmus / 18 \\
                 Rationale Binomialkoeffizienten / 22 \\
                 Kettenbruchdarstellungen reeller Zahlen / 28 \\
                 Genaue Kettenbruchdarstellungen von quadratischen
                 Irrationalit{\"a}ten / 33 \\
                 Teil II: Iteration / 39 \\
                 Iteration / 40 \\
                 Iteration mit Aitken-Beschleunigung / 45 \\
                 Aitken--Steffensen-Iteration / 50 \\
                 Newton-Iteration f{\"u}r Wurzeln komplexer Zahlen / 55
                 \\
                 Teil III: Polynome / 61 \\
                 Der Horner-Algorithmus 6 / 2 \\
                 Das Newton-Verfahren bei Polynomen / 66 \\
                 Bernoulli-Verfahren: Eine reelle dominante Nullstelle /
                 71 \\
                 Bernoulli-Verfahren: Zwei konjugiert komplexe dominante
                 Nullstellen / 76 \\
                 Der Quotienten--Differenzen-Algorithmus / 82 \\
                 Der Routh-Algorithmus / 87 \\
                 Der Schur--Cohn-Algorithmus I / 92 \\
                 Der Schur--Cohn-Algorithmus II / 97 \\
                 Teil IV: Potenzreihen / 101 \\
                 Reziproke Potenzreihe / 102 \\
                 Potenz einer Potenzreihe / 111 \\
                 Exponentiation einer Potenzreihe / 118 \\
                 Teil V: Integration / 123 \\
                 Numerische Integration mit Schrittverfeinerung / 124
                 \\
                 Der Romberg-Algorithmus / 129 \\
                 Die Planasche Summationsformel / 136 \\
                 Eine Differentialgleichung erster Ordnung: Trapezregel
                 / 143 \\
                 Autonome Differentialgleichung zweiter Ordnung ohne
                 erste Ableitung / 150 \\
                 Lineare Differentialgleichung zweiter Ordnung / 155 \\
                 Teil VI: Spezielle Konstanten und Funktionen / 161 \\
                 Log-Arcsinus-Algorithmus / 162 \\
                 Die Gamma-Funktion / 167 \\
                 Unvollst{\"a}ndige Gamma-Funktion / 174 \\
                 Die Fehlerfunktion / 181 \\
                 Vollst{\"a}ndige elliptische Integrale / 187 \\
                 Besselfunktionen ganzzahliger Ordnung / 191 \\
                 Besselfunktionen beliebiger Ordnung / 196 \\
                 Besselfunktionen: Asymptotische Reihe / 201 \\
                 Die Riemannsche Zetafunktion auf der kritischen Geraden
                 / 207 \\
                 Stichwortverzeichnis / 213",
}


bibtype: book
filename: elefunt.bib
label: Higgins:1977:CBP
author: John Rowland Higgins
title: Completeness and basis properties of sets of special functions
publisher: pub-CAMBRIDGE
address: pub-CAMBRIDGE:adr
pages: x + 134
year: 1977
bibdate: Sat Oct 30 16:52:55 MDT 2010
bibsource: carmin.sudoc.abes.fr:210/ABES-Z39-PUBLIC; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.30 16:52:55 MDT
acknowledgement: ack-nhfb
rawauthor: John Rowland Higgins
rawtitle: Completeness and basis properties of sets of special functions
ISBN:
0-521-21376-2 (hardcover), 0-521-60488-5 (paperback) OR 0521213762 (hardcover), 0521604885 (paperback)

ISBN13:
978-0-521-21376-9 (hardcover), 978-0-521-60488-8 (paperback) OR 9780521213769 (hardcover), 9780521604888 (paperback)

entry:
@Book{Higgins:1977:CBP,
  author =       "John Rowland Higgins",
  title =        "Completeness and basis properties of sets of special
                 functions",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  pages =        "x + 134",
  year =         "1977",
  ISBN =         "0-521-21376-2 (hardcover), 0-521-60488-5 (paperback)",
  ISBN-13 =      "978-0-521-21376-9 (hardcover), 978-0-521-60488-8
                 (paperback)",
  LCCN =         "????",
  bibdate =      "Sat Oct 30 16:52:55 MDT 2010",
  bibsource =    "carmin.sudoc.abes.fr:210/ABES-Z39-PUBLIC;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Hill:1977:AIB
author: G. W. Hill
title: Algorithm 518: Incomplete Bessel Function $ I_0 $. The von Mises Distribution [S14]
journal: j-TOMS
volume: 3
number: 3
pages: 279--284
month: sep
monthnumber: 9
year: 1977
CODEN: ACMSCU
DOI: https://doi.org/10.1145/355744.355753
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Sat Oct 24 15:46:06 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1998.10.24 15:46:06 ???
fjournal: ACM Transactions on Mathematical Software (TOMS)
remark: Fullerton: Adjustable-accuracy 50-statement FORTRAN subprogram.
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: G. W. Hill
rawtitle: {Algorithm 518}: Incomplete {Bessel} Function {$ I_0 $}. {The von Mises} Distribution [{S14}]
entry:
@Article{Hill:1977:AIB,
  author =       "G. W. Hill",
  title =        "{Algorithm 518}: Incomplete {Bessel} Function {$ I_0
                 $}. {The von Mises} Distribution [{S14}]",
  journal =      j-TOMS,
  volume =       "3",
  number =       "3",
  pages =        "279--284",
  month =        sep,
  year =         "1977",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355744.355753",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Oct 24 15:46:06 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  remark =       "Fullerton: Adjustable-accuracy 50-statement FORTRAN
                 subprogram.",
}


bibtype: article
filename: elefunt.bib
label: Hinden:1977:PAR
author: Harvey J. Hinden
journal: j-FIB-QUART
volume: 15
number: 2
pages: 112, 152
month: apr
monthnumber: 4
year: 1977
CODEN: FIBQAU
ISSN: 0015-0517 OR 00150517
ISSNL: 0015-0517 OR 00150517
bibdate: Thu Oct 20 17:59:17 MDT 2011
bibtimestamp: 2011.10.20 17:59:17 MDT
URL: http://www.fq.math.ca/Scanned/15-2/hinden-a.pdf
fjournal: The Fibonacci Quarterly. Official Organ of the Fibonacci Association
acknowledgement: ack-nhfb
ajournal: Fib. Quart
journalURL: http://www.fq.math.ca/
rawauthor: Harvey J. Hinden
title:
Phi Again: a Relationship Between the Golden Ratio and the Limit of a Ratio of Modified Bessel Functions

bibsource:
http://www.fq.math.ca/15-2.html; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fibquart.bib

rawtitle:
Phi Again: a Relationship Between the Golden Ratio and the Limit of a Ratio of Modified {Bessel} Functions

entry:
@Article{Hinden:1977:PAR,
  author =       "Harvey J. Hinden",
  title =        "Phi Again: a Relationship Between the Golden Ratio and
                 the Limit of a Ratio of Modified {Bessel} Functions",
  journal =      j-FIB-QUART,
  volume =       "15",
  number =       "2",
  pages =        "112, 152",
  month =        apr,
  year =         "1977",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  bibdate =      "Thu Oct 20 17:59:17 MDT 2011",
  bibsource =    "http://www.fq.math.ca/15-2.html;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fibquart.bib",
  URL =          "http://www.fq.math.ca/Scanned/15-2/hinden-a.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly. Official Organ of the
                 Fibonacci Association",
  journal-URL =  "http://www.fq.math.ca/",
}


bibtype: article
filename: elefunt.bib
label: Ismail:1977:IRC
author: Mourad E. H. Ismail
title: Integral representations and complete monotonicity of various quotients of Bessel functions
journal: j-CAN-J-MATH
volume: 29
pages: 1198--1207
year: 1977
CODEN: CJMAAB
DOI: https://doi.org/10.4153/CJM-1977-119-5
ISSN: 0008-414X (print), 1496-4279 (electronic) OR 0008414X (print), 14964279 (electronic)
ISSNL: 0008-414X OR 0008414X
bibdate: Sat Sep 10 15:38:50 MDT 2011
bibtimestamp: 2011.09.10 15:38:50 MDT
fjournal: Canadian Journal of Mathematics = Journal canadien de mathematiques
acknowledgement: ack-nhfb
journalURL: http://cms.math.ca/cjm/
rawauthor: Mourad E. H. Ismail
rawtitle: Integral representations and complete monotonicity of various quotients of {Bessel} functions
bibsource:
http://cms.math.ca/cjm/v29/; https://www.math.utah.edu/pub/tex/bib/canjmath1970.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Ismail:1977:IRC,
  author =       "Mourad E. H. Ismail",
  title =        "Integral representations and complete monotonicity of
                 various quotients of {Bessel} functions",
  journal =      j-CAN-J-MATH,
  volume =       "29",
  number =       "??",
  pages =        "1198--1207",
  month =        "????",
  year =         "1977",
  CODEN =        "CJMAAB",
  DOI =          "https://doi.org/10.4153/CJM-1977-119-5",
  ISSN =         "0008-414X (print), 1496-4279 (electronic)",
  ISSN-L =       "0008-414X",
  bibdate =      "Sat Sep 10 15:38:50 MDT 2011",
  bibsource =    "http://cms.math.ca/cjm/v29/;
                 https://www.math.utah.edu/pub/tex/bib/canjmath1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Canadian Journal of Mathematics = Journal canadien de
                 math{\'e}matiques",
  journal-URL =  "http://cms.math.ca/cjm/",
}


bibtype: article
filename: elefunt.bib
label: Jansen:1977:RLF
author: J. K. M. Jansen
title: Remark on ``Algorithm 259: Legendre Functions for Arguments Larger than One''
journal: j-TOMS
volume: 3
number: 2
pages: 204--250
month: jun
monthnumber: 6
year: 1977
CODEN: ACMSCU
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Tue Feb 06 05:28:08 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1996.02.06 05:28:08 ???
note: See cite Gautschi:1965:ALF.
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: J. K. M. Jansen
rawnote: See \cite{Gautschi:1965:ALF}.
rawtitle: Remark on ``{Algorithm 259: Legendre Functions for Arguments Larger than One}''
entry:
@Article{Jansen:1977:RLF,
  author =       "J. K. M. Jansen",
  title =        "Remark on ``{Algorithm 259: Legendre Functions for
                 Arguments Larger than One}''",
  journal =      j-TOMS,
  volume =       "3",
  number =       "2",
  pages =        "204--250",
  month =        jun,
  year =         "1977",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Feb 06 05:28:08 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Gautschi:1965:ALF}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: book
filename: elefunt.bib
label: Luke:1977:ACM
author: Yudell L. Luke
title: Algorithms for the Computation of Mathematical Functions
publisher: pub-ACADEMIC
address: pub-ACADEMIC:adr
pages: xiii + 284
year: 1977
ISBN: 0-12-459940-0 OR 0124599400
ISBN13: 978-0-12-459940-6 OR 9780124599406
LCCN: QA351 .L7961
bibdate: Wed Dec 15 10:38:19 1993
bibtimestamp: 1993.12.15 10:38:19 ???
acknowledgement: ack-nhfb
rawauthor: Yudell L. Luke
rawtitle: Algorithms for the Computation of Mathematical Functions
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/master.bib; https://www.math.utah.edu/pub/tex/bib/mathcw.bib

TOC:
Preface / xi 1: Basic Formulas / 1 1.1 Introduction / 1 1.2 The Generalized Hypergeometric Function and the $G$-Function / 1 1.3 Expansion of $_pF_q(z)$ and $G^q - r, 1_p + 1, q(z)$, $r = 0$ or $r = 1$, in Series of Chebyshev Polynomials of the First Kind / 4 1.4 Efficient Evaluation of Series of Chebyshev Polynomials / 17 1.5 Rational Approximations for Generalized Hypergeometric Functions / 20 1.6 The Pade Table / 27 1.7 Computations of and Checks on Coefficients and Tables / 29 1.8 Tables of the Functions $e^-zeta $, and $e^-xi $ / 35 2: Identification of Functions / 41 2.1 Introduction / 41 2.2 The Generalized Hypergeometric Function $_pF_q(z)$ / 41 2.3 The G-Function / 47 2.4 Miscellaneous Functions / 48 3: General Remarks on the Algorithms and Programs / 49 3.1 Introduction / 49 3.2 Precision and Complex Arithmetic / 49 4: Chebyshev Coefficients for $_2F_1(a.b;c;z)$ / 52 5: Coefficients for the Expansion of the Confluent Hypergeometric Function $_1F_1(a;c;z)$ in Ascending Series of Chebyshev Polynomials / 70 6: Chebyshev Coefficients for $_0F_1(c;z)$ / 77 7: Coefficients for the Expansion of $_1F_2(a;b,c;z)$ in Ascending Series of Chebyshev Polynomials / 82 8: Coefficients for the Expansion of the Confluent Hypergeometric Functions $U(a;c;z)$ and $_1F_1(a;c;-z)$ in Descending Series of Chebyshev Polynomials / 88 9: Coefficients for the Expansion of the Functions $G^m,1_1,3(z^2/4|^1_a,b,c)$, $m = 3$ or $m = 2$, in Descending Series of Chebyshev Polynomials / 101 10: Differential and Integral Properties of Expansions in Series of Chebyshev Polynomials of the First Kind / 116 11: Expansion of Exponential Type Integrals in Series of Chebyshev Polynomials of the First Kind / 126 11.1 Introduction / 126 11.2 The Representation for $g(x)$ / 127 11.3 The Representation for $G(x)$ / 129 11.4 Exponential Type Integrals Involving Logarithms / 133 11.5 Numerical Examples / 135 11.6 Errata / 139 12: Conversion of a Power Series into a Series of Chebyshev Polynomials of the First Kind / 154 13: Rational Approximations for $_2F_1(a,b;c;-z)$ / 159 14: Pade Approximations for $_2F_1(1,b;c;-z)$ / 174 15: Rational Approximations for $_1F_1(a;c;-z)$ / 182 16: Pade Approximations for $_1F_1(1;c;-z)$ / 192 17: Rational Approximations for Bessel Functions of the First Kind / 203 18: Pade Approximations for $I_nu + 1(z)/I_nu (z)$ / 220 19: Evaluation of Bessel Functions of the First Kind by Use of the Backward Recurrence Formula 19.1 Introduction / 230 19.2 Backward Recurrence Schemata for $I_nu (z)$ and $J_nu (z)$ / 230 19.3 Numerical Examples / 240 19.4 Mathematical Description of Programs / 243 19.4.1 Evaluation of Functions Related to $I_m + nu (z)$ and $J_m + nu (z)$ / 243 19.4.2 Evaluation of Functions Related to $e^-lI_m + nu (z)$ / 245 20: Rational Approximations for $z^aU(a;1 + a - b;z)$ / 252 21: Pade Approximations for $z U(1;2-b;z)$ / 265 Appendices Bibliography / 280 Notation Index / 281 Subject Index / 283

rawTOC:
Preface / xi \\ 1: Basic Formulas / 1 \\ 1.1 Introduction / 1 \\ 1.2 The Generalized Hypergeometric Function and the $G$-Function / 1 \\ 1.3 Expansion of $_pF_q(z)$ and $G^{q - r, 1}_{p + 1, q}(z)$, $r = 0$ or $r = 1$, in Series of Chebyshev Polynomials of the First Kind / 4 \\ 1.4 Efficient Evaluation of Series of Chebyshev Polynomials / 17 \\ 1.5 Rational Approximations for Generalized Hypergeometric Functions / 20 \\ 1.6 The Pad{\'e} Table / 27 \\ 1.7 Computations of and Checks on Coefficients and Tables / 29 \\ 1.8 Tables of the Functions $e^{-\zeta}$, and $e^{-\xi}$ / 35 \\ 2: Identification of Functions / 41 \\ 2.1 Introduction / 41 \\ 2.2 The Generalized Hypergeometric Function $_pF_q(z)$ / 41 \\ 2.3 The G-Function / 47 \\ 2.4 Miscellaneous Functions / 48 \\ 3: General Remarks on the Algorithms and Programs / 49 \\ 3.1 Introduction / 49 \\ 3.2 Precision and Complex Arithmetic / 49 \\ 4: Chebyshev Coefficients for $_2F_1(a.b;c;z)$ / 52 \\ 5: Coefficients for the Expansion of the Confluent Hypergeometric Function $_1F_1(a;c;z)$ in Ascending Series of Chebyshev Polynomials / 70 \\ 6: Chebyshev Coefficients for $_0F_1(c;z)$ / 77 \\ 7: Coefficients for the Expansion of $_1F_2(a;b,c;z)$ in Ascending Series of Chebyshev Polynomials / 82 \\ 8: Coefficients for the Expansion of the Confluent Hypergeometric Functions $U(a;c;z)$ and $_1F_1(a;c;-z)$ in Descending Series of Chebyshev Polynomials / 88 \\ 9: Coefficients for the Expansion of the Functions $G^{m,1}_{1,3}(z^2/4|^1_{a,b,c})$, $m = 3$ or $m = 2$, in Descending Series of Chebyshev Polynomials / 101 \\ 10: Differential and Integral Properties of Expansions in Series of Chebyshev Polynomials of the First Kind / 116 \\ 11: Expansion of Exponential Type Integrals in Series of Chebyshev Polynomials of the First Kind / 126 \\ 11.1 Introduction / 126 \\ 11.2 The Representation for $g(x)$ / 127 \\ 11.3 The Representation for $G(x)$ / 129 \\ 11.4 Exponential Type Integrals Involving Logarithms / 133 \\ 11.5 Numerical Examples / 135 \\ 11.6 Errata / 139 \\ 12: Conversion of a Power Series into a Series of Chebyshev Polynomials of the First Kind / 154 \\ 13: Rational Approximations for $_2F_1(a,b;c;-z)$ / 159 \\ 14: Pad{\'e} Approximations for $_2F_1(1,b;c;-z)$ / 174 \\ 15: Rational Approximations for $_1F_1(a;c;-z)$ / 182 \\ 16: Pad{\'e} Approximations for $_1F_1(1;c;-z)$ / 192 \\ 17: Rational Approximations for Bessel Functions of the First Kind / 203 \\ 18: Pad{\'e} Approximations for $I_{\nu + 1}(z)/I_\nu(z)$ / 220 \\ 19: Evaluation of Bessel Functions of the First Kind by Use of the Backward Recurrence Formula \\ 19.1 Introduction / 230 \\ 19.2 Backward Recurrence Schemata for $I_\nu(z)$ and $J_\nu(z)$ / 230 \\ 19.3 Numerical Examples / 240 \\ 19.4 Mathematical Description of Programs / 243 \\ 19.4.1 Evaluation of Functions Related to $I_{m + \nu}(z)$ and $J_{m + \nu}(z)$ / 243 \\ 19.4.2 Evaluation of Functions Related to $e^{-l}I_{m + \nu}(z)$ / 245 \\ 20: Rational Approximations for $z^aU(a;1 + a - b;z)$ / 252 \\ 21: Pad{\'e} Approximations for $z U(1;2-b;z)$ / 265 \\ Appendices \\ Bibliography / 280 \\ Notation Index / 281 \\ Subject Index / 283

entry:
@Book{Luke:1977:ACM,
  author =       "Yudell L. Luke",
  title =        "Algorithms for the Computation of Mathematical
                 Functions",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "xiii + 284",
  year =         "1977",
  ISBN =         "0-12-459940-0",
  ISBN-13 =      "978-0-12-459940-6",
  LCCN =         "QA351 .L7961",
  bibdate =      "Wed Dec 15 10:38:19 1993",
  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/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
  acknowledgement = ack-nhfb,
  tableofcontents = "Preface / xi \\
                 1: Basic Formulas / 1 \\
                 1.1 Introduction / 1 \\
                 1.2 The Generalized Hypergeometric Function and the
                 $G$-Function / 1 \\
                 1.3 Expansion of $_pF_q(z)$ and $G^{q - r, 1}_{p + 1,
                 q}(z)$, $r = 0$ or $r = 1$, in Series of Chebyshev
                 Polynomials of the First Kind / 4 \\
                 1.4 Efficient Evaluation of Series of Chebyshev
                 Polynomials / 17 \\
                 1.5 Rational Approximations for Generalized
                 Hypergeometric Functions / 20 \\
                 1.6 The Pad{\'e} Table / 27 \\
                 1.7 Computations of and Checks on Coefficients and
                 Tables / 29 \\
                 1.8 Tables of the Functions $e^{-\zeta}$, and
                 $e^{-\xi}$ / 35 \\
                 2: Identification of Functions / 41 \\
                 2.1 Introduction / 41 \\
                 2.2 The Generalized Hypergeometric Function $_pF_q(z)$
                 / 41 \\
                 2.3 The G-Function / 47 \\
                 2.4 Miscellaneous Functions / 48 \\
                 3: General Remarks on the Algorithms and Programs / 49
                 \\
                 3.1 Introduction / 49 \\
                 3.2 Precision and Complex Arithmetic / 49 \\
                 4: Chebyshev Coefficients for $_2F_1(a.b;c;z)$ / 52 \\
                 5: Coefficients for the Expansion of the Confluent
                 Hypergeometric Function $_1F_1(a;c;z)$ in Ascending
                 Series of Chebyshev Polynomials / 70 \\
                 6: Chebyshev Coefficients for $_0F_1(c;z)$ / 77 \\
                 7: Coefficients for the Expansion of $_1F_2(a;b,c;z)$
                 in Ascending Series of Chebyshev Polynomials / 82 \\
                 8: Coefficients for the Expansion of the Confluent
                 Hypergeometric Functions $U(a;c;z)$ and $_1F_1(a;c;-z)$
                 in Descending Series of Chebyshev Polynomials / 88 \\
                 9: Coefficients for the Expansion of the Functions
                 $G^{m,1}_{1,3}(z^2/4|^1_{a,b,c})$, $m = 3$ or $m = 2$,
                 in Descending Series of Chebyshev Polynomials / 101 \\
                 10: Differential and Integral Properties of Expansions
                 in Series of Chebyshev Polynomials of the First Kind /
                 116 \\
                 11: Expansion of Exponential Type Integrals in Series
                 of Chebyshev Polynomials of the First Kind / 126 \\
                 11.1 Introduction / 126 \\
                 11.2 The Representation for $g(x)$ / 127 \\
                 11.3 The Representation for $G(x)$ / 129 \\
                 11.4 Exponential Type Integrals Involving Logarithms /
                 133 \\
                 11.5 Numerical Examples / 135 \\
                 11.6 Errata / 139 \\
                 12: Conversion of a Power Series into a Series of
                 Chebyshev Polynomials of the First Kind / 154 \\
                 13: Rational Approximations for $_2F_1(a,b;c;-z)$ / 159
                 \\
                 14: Pad{\'e} Approximations for $_2F_1(1,b;c;-z)$ / 174
                 \\
                 15: Rational Approximations for $_1F_1(a;c;-z)$ / 182
                 \\
                 16: Pad{\'e} Approximations for $_1F_1(1;c;-z)$ / 192
                 \\
                 17: Rational Approximations for Bessel Functions of the
                 First Kind / 203 \\
                 18: Pad{\'e} Approximations for $I_{\nu +
                 1}(z)/I_\nu(z)$ / 220 \\
                 19: Evaluation of Bessel Functions of the First Kind by
                 Use of the Backward Recurrence Formula \\
                 19.1 Introduction / 230 \\
                 19.2 Backward Recurrence Schemata for $I_\nu(z)$ and
                 $J_\nu(z)$ / 230 \\
                 19.3 Numerical Examples / 240 \\
                 19.4 Mathematical Description of Programs / 243 \\
                 19.4.1 Evaluation of Functions Related to $I_{m +
                 \nu}(z)$ and $J_{m + \nu}(z)$ / 243 \\
                 19.4.2 Evaluation of Functions Related to $e^{-l}I_{m +
                 \nu}(z)$ / 245 \\
                 20: Rational Approximations for $z^aU(a;1 + a - b;z)$ /
                 252 \\
                 21: Pad{\'e} Approximations for $z U(1;2-b;z)$ / 265
                 \\
                 Appendices \\
                 Bibliography / 280 \\
                 Notation Index / 281 \\
                 Subject Index / 283",
  wrongisbn =    "0-12-459940-6",
}


bibtype: article
filename: elefunt.bib
label: Marsaglia:1977:SMG
author: George Marsaglia
title: The squeeze method for generating gamma variates
journal: j-COMPUT-MATH-APPL
volume: 3
number: 4
pages: 321--325
year: 1977
CODEN: CMAPDK
DOI: https://doi.org/10.1016/0898-1221(77)90089-X
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
MRclass: 65C10
MRnumber: 58 \#13613
bibdate: Mon Oct 24 11:37:20 2011
bibtimestamp: 2011.10.24 11:37:20 ???
fjournal: Computers and Mathematics with Applications
ZMnumber: 0384.65005
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/08981221
ZMclass: *65C10 Random number generation 60E05 General theory of probability distributions
rawauthor: George Marsaglia
rawtitle: The squeeze method for generating gamma variates
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; MathSciNet database

abstract:
This paper describes an exact method for computer generation of random variables with a gamma distribution. The method is based on the Wilson--Hilferty transformation and an improvement on the rejection technique. The idea is to ``squeeze'' a target density between two functions, the top one easy to sample from, the bottom one easy to evaluate.

rawabstract:
This paper describes an exact method for computer generation of random variables with a gamma distribution. The method is based on the Wilson--Hilferty transformation and an improvement on the rejection technique. The idea is to ``squeeze'' a target density between two functions, the top one easy to sample from, the bottom one easy to evaluate.

entry:
@Article{Marsaglia:1977:SMG,
  author =       "George Marsaglia",
  title =        "The squeeze method for generating gamma variates",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "3",
  number =       "4",
  pages =        "321--325",
  year =         "1977",
  CODEN =        "CMAPDK",
  DOI =          "https://doi.org/10.1016/0898-1221(77)90089-X",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  MRclass =      "65C10",
  MRnumber =     "58 \#13613",
  bibdate =      "Mon Oct 24 11:37:20 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 MathSciNet database",
  ZMnumber =     "0384.65005",
  abstract =     "This paper describes an exact method for computer
                 generation of random variables with a gamma
                 distribution. The method is based on the
                 Wilson--Hilferty transformation and an improvement on
                 the rejection technique. The idea is to ``squeeze'' a
                 target density between two functions, the top one easy
                 to sample from, the bottom one easy to evaluate.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
  ZMclass =      "*65C10 Random number generation 60E05 General theory
                 of probability distributions",
}


bibtype: article
filename: elefunt.bib
label: McCarthy:1977:OAE
author: D. P. McCarthy
title: The optimal algorithm to evaluate $ x^n $ using elementary multiplication methods
journal: j-MATH-COMPUT
volume: 31
number: 137
pages: 251--256
month: jan
monthnumber: 1
year: 1977
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
classcodes: C4120 (Functional analysis); C4240 (Programming and algorithm theory)
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: D. P. McCarthy
rawtitle: The optimal algorithm to evaluate $ x^n $ using elementary multiplication methods
keywords:
computational complexity; function evaluation; optimal multiplication chains; symbolic algebraic manipulation

entry:
@Article{McCarthy:1977:OAE,
  author =       "D. P. McCarthy",
  title =        "The optimal algorithm to evaluate $ x^n $ using
                 elementary multiplication methods",
  journal =      j-MATH-COMPUT,
  volume =       "31",
  number =       "137",
  pages =        "251--256",
  month =        jan,
  year =         "1977",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "C4120 (Functional analysis); C4240 (Programming and
                 algorithm theory)",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "computational complexity; function evaluation; optimal
                 multiplication chains; symbolic algebraic
                 manipulation",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Ng:1977:CAL
author: E. W. Ng
title: Computations and Applications of Linear Hypergeometric Transformations
journal: j-COMPUT-MATH-APPL
volume: 3
number: 1
pages: 65--70
year: 1977
CODEN: CMAPDK
DOI: https://doi.org/10.1016/0898-1221(77)90115-8
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Sat Oct 30 09:27:55 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.30 09:27:55 ???
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/08981221
rawauthor: E. W. Ng
rawtitle: Computations and Applications of Linear Hypergeometric Transformations
abstract:
Linear transformations are well-known in the theory of hypergeometric functions. In this note, it is indicated, both by analyses and by supporting numerical experiments, how these transformations can be applied to the computation of Legendre's functions, the incomplete Beta function, and the variance-ratio probability distribution function. It is shown that a simple transformation can in many cases cause dramatic improvement in computation.

rawabstract:
Linear transformations are well-known in the theory of hypergeometric functions. In this note, it is indicated, both by analyses and by supporting numerical experiments, how these transformations can be applied to the computation of Legendre's functions, the incomplete Beta function, and the variance-ratio probability distribution function. It is shown that a simple transformation can in many cases cause dramatic improvement in computation.

entry:
@Article{Ng:1977:CAL,
  author =       "E. W. Ng",
  title =        "Computations and Applications of Linear Hypergeometric
                 Transformations",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "3",
  number =       "1",
  pages =        "65--70",
  year =         "1977",
  CODEN =        "CMAPDK",
  DOI =          "https://doi.org/10.1016/0898-1221(77)90115-8",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Sat Oct 30 09:27:55 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "Linear transformations are well-known in the theory of
                 hypergeometric functions. In this note, it is
                 indicated, both by analyses and by supporting numerical
                 experiments, how these transformations can be applied
                 to the computation of Legendre's functions, the
                 incomplete Beta function, and the variance-ratio
                 probability distribution function. It is shown that a
                 simple transformation can in many cases cause dramatic
                 improvement in computation.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}


bibtype: article
filename: elefunt.bib
label: Page:1977:MAC
author: E. Page
journal: j-APPL-STAT
volume: 26
number: 1
pages: 75--76
year: 1977
CODEN: APSTAG
ISSN: 0035-9254 (print), 1467-9876 (electronic) OR 00359254 (print), 14679876 (electronic)
ISSNL: 0035-9254 OR 00359254
bibdate: Sat Apr 21 10:21:55 MDT 2001
bibtimestamp: 2001.04.21 10:21:55 MDT
fjournal: Applied Statistics
acknowledgement: ack-nhfb
journalURL: http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-9876/issues
rawauthor: E. Page
title:
Miscellanea: Approximations to the Cumulative Normal Function and its Inverse for Use on a Pocket Calculator

bibsource:
https://www.math.utah.edu/pub/tex/bib/as1970.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database

rawtitle:
Miscellanea: Approximations to the Cumulative Normal Function and its Inverse for Use on a Pocket Calculator

entry:
@Article{Page:1977:MAC,
  author =       "E. Page",
  title =        "Miscellanea: Approximations to the Cumulative Normal
                 Function and its Inverse for Use on a Pocket
                 Calculator",
  journal =      j-APPL-STAT,
  volume =       "26",
  number =       "1",
  pages =        "75--76",
  year =         "1977",
  CODEN =        "APSTAG",
  ISSN =         "0035-9254 (print), 1467-9876 (electronic)",
  ISSN-L =       "0035-9254",
  bibdate =      "Sat Apr 21 10:21:55 MDT 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/as1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Statistics",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-9876/issues",
}


bibtype: article
filename: elefunt.bib
label: Pexton:1977:RTTa
author: Robert L. Pexton and Arno D. Steiger
title: Roots of two transcendental equations involving spherical Bessel functions
journal: j-MATH-COMPUT
volume: 31
number: 139
pages: 752--753
month: jul
monthnumber: 7
year: 1977
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
keywords: Bessel functions; root; spherical Bessel functions; transcendental equations
acknowledgement: ack-nhfb
classcodes: C1110 (Algebra)
corpsource: Univ. of California, Livermore, CA, USA
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: Robert L. Pexton and Arno D. Steiger
rawtitle: Roots of two transcendental equations involving spherical {Bessel} functions
entry:
@Article{Pexton:1977:RTTa,
  author =       "Robert L. Pexton and Arno D. Steiger",
  title =        "Roots of two transcendental equations involving
                 spherical {Bessel} functions",
  journal =      j-MATH-COMPUT,
  volume =       "31",
  number =       "139",
  pages =        "752--753",
  month =        jul,
  year =         "1977",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "C1110 (Algebra)",
  corpsource =   "Univ. of California, Livermore, CA, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Bessel functions; root; spherical Bessel functions;
                 transcendental equations",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: inproceedings
filename: elefunt.bib
label: Randazzo:1977:DFE
author: D. J. Randazzo
booktitle: Numerical analysis (Proceedings of the Colloquium, Lausanne, 1976)
title: Data fits with exponential functions
volume: 37
publisher: pub-BIRKHAUSER
address: pub-BIRKHAUSER:adr
pages: 77--94
year: 1977
ISBN: 3-7643-0939-3 OR 3764309393
ISBN13: 978-3-7643-0939-8 OR 9783764309398
MRclass: 65D15
MRnumber: 468111
MRreviewer: C. W. Clenshaw
bibdate: Mon Nov 13 08:14:42 2023
bibtimestamp: 2023.11.13 08:14:42 ???
series: Internat. Ser. Numer. Math.
acknowledgement: ack-nhfb
rawauthor: D. J. Randazzo
rawbooktitle: Numerical analysis ({Proceedings of the Colloquium, Lausanne, 1976})
rawtitle: Data fits with exponential functions
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/c/clenshaw-charles-w.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@InProceedings{Randazzo:1977:DFE,
  author =       "D. J. Randazzo",
  booktitle =    "Numerical analysis ({Proceedings of the Colloquium,
                 Lausanne, 1976})",
  title =        "Data fits with exponential functions",
  volume =       "37",
  publisher =    pub-BIRKHAUSER,
  address =      pub-BIRKHAUSER:adr,
  pages =        "77--94",
  year =         "1977",
  ISBN =         "3-7643-0939-3",
  ISBN-13 =      "978-3-7643-0939-8",
  MRclass =      "65D15",
  MRnumber =     "468111",
  MRreviewer =   "C. W. Clenshaw",
  bibdate =      "Mon Nov 13 08:14:42 2023",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/clenshaw-charles-w.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Internat. Ser. Numer. Math.",
  acknowledgement = ack-nhfb,
  reviewer-dates = "Charles William Clenshaw (15 March 1926--23
                 September 2004)",
}


bibtype: article
filename: elefunt.bib
label: Schett:1977:RFT
author: Alois Schett
title: Recurrence formula of the Taylor series expansion coefficients of the Jacobian elliptic functions
journal: j-MATH-COMPUT
volume: 31
number: 140
pages: 1003--1005
month: oct
monthnumber: 10
year: 1977
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
classcodes: C1110 (Algebra)
corpsource: CENS, Gif-sur-Yvette, France
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: Alois Schett
keywords:
elliptic functions; functions; Jacobian elliptic; peak; recurrence formula; run up; Taylor series expansion coefficients

rawtitle:
Recurrence formula of the {Taylor} series expansion coefficients of the {Jacobian} elliptic functions

entry:
@Article{Schett:1977:RFT,
  author =       "Alois Schett",
  title =        "Recurrence formula of the {Taylor} series expansion
                 coefficients of the {Jacobian} elliptic functions",
  journal =      j-MATH-COMPUT,
  volume =       "31",
  number =       "140",
  pages =        "1003--1005",
  month =        oct,
  year =         "1977",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "C1110 (Algebra)",
  corpsource =   "CENS, Gif-sur-Yvette, France",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "elliptic functions; functions; Jacobian elliptic;
                 peak; recurrence formula; run up; Taylor series
                 expansion coefficients",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Schindler:1977:CCS
author: Susan Schindler and R. Mirman
title: The Clebsch--Gordan coefficients of $ S_n $
journal: j-J-MATH-PHYS
volume: 18
number: 8
pages: 1697--1704
month: aug
monthnumber: 8
year: 1977
CODEN: JMAPAQ
DOI: https://doi.org/10.1063/1.523470
ISSNL: 0022-2488 OR 00222488
bibdate: Fri Jan 2 14:59:17 MST 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1998.01.02 14:59:17 MST
fjournal: Journal of Mathematical Physics
keywords: $S_n$ group; Clebsch Gordan coefficients; Clebsch--Gordan coefficients; working triplets
acknowledgement: ack-nhfb
corpsource: Baruch Coll., City Univ. of New York, NY, USA
journalURL: http://jmp.aip.org/
treatment: T Theoretical or Mathematical
rawauthor: Susan Schindler and R. Mirman
rawtitle: The {Clebsch--Gordan} coefficients of {$ S_n $}
abstract:
Ordering schemes for the frames and tableaux of $ S_n $ are presented, and some results, expressible in terms of these, are developed. A formula is derived for the sign function on tableaux. A table of the nonzero Clebsch--Gordon coefficients for the ''working triplets'' is given. Methods are described, and a needed table supplied, for finding the other coefficients from the tabulated ones. The values are for $ n = 2, ldots , 6 $, with the coefficients for $ n = 6 $ relegated to PAPS.

rawabstract:
Ordering schemes for the frames and tableaux of $ S_n $ are presented, and some results, expressible in terms of these, are developed. A formula is derived for the sign function on tableaux. A table of the nonzero Clebsch--Gordon coefficients for the ''working triplets'' is given. Methods are described, and a needed table supplied, for finding the other coefficients from the tabulated ones. The values are for $ n = 2, \ldots {}, 6 $, with the coefficients for $ n = 6 $ relegated to PAPS.

entry:
@Article{Schindler:1977:CCS,
  author =       "Susan Schindler and R. Mirman",
  title =        "The {Clebsch--Gordan} coefficients of {$ S_n $}",
  journal =      j-J-MATH-PHYS,
  volume =       "18",
  number =       "8",
  pages =        "1697--1704",
  month =        aug,
  year =         "1977",
  CODEN =        "JMAPAQ",
  DOI =          "https://doi.org/10.1063/1.523470",
  ISSN =         "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
  ISSN-L =       "0022-2488",
  bibdate =      "Fri Jan 2 14:59:17 MST 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "Ordering schemes for the frames and tableaux of $ S_n
                 $ are presented, and some results, expressible in terms
                 of these, are developed. A formula is derived for the
                 sign function on tableaux. A table of the nonzero
                 Clebsch--Gordon coefficients for the ''working
                 triplets'' is given. Methods are described, and a
                 needed table supplied, for finding the other
                 coefficients from the tabulated ones. The values are
                 for $ n = 2, \ldots {}, 6 $, with the coefficients for
                 $ n = 6 $ relegated to PAPS.",
  acknowledgement = ack-nhfb,
  classification = "A0365F (Algebraic methods in quantum theory); A1130L
                 (Other internal and higher symmetries in particle
                 physics)",
  corpsource =   "Baruch Coll., City Univ. of New York, NY, USA",
  fjournal =     "Journal of Mathematical Physics",
  journal-URL =  "http://jmp.aip.org/",
  keywords =     "$S_n$ group; Clebsch Gordan coefficients;
                 Clebsch--Gordan coefficients; working triplets",
  pubcountry =   "USA",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: inproceedings
filename: elefunt.bib
label: Schonfelder:1977:PTS
author: J. L. Schonfelder
title: The Production and Testing of Special Function Software in the NAG Library
crossref: Cowell:1977:PMS
pages: 425--451
year: 1977
bibdate: Sat Oct 30 10:24:29 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.30 10:24:29 ???
acknowledgement: ack-nhfb
rawauthor: J. L. Schonfelder
rawtitle: The Production and Testing of Special Function Software in the {NAG} Library
entry:
@InProceedings{Schonfelder:1977:PTS,
  author =       "J. L. Schonfelder",
  title =        "The Production and Testing of Special Function
                 Software in the {NAG} Library",
  crossref =     "Cowell:1977:PMS",
  pages =        "425--451",
  year =         "1977",
  bibdate =      "Sat Oct 30 10:24:29 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
}


bibtype: article
filename: elefunt.bib
label: Sharma:1977:GMA
author: R. R. Sharma and Bahman Zohuri
title: A general method for an accurate evaluation of exponential integrals $ E_1 (x), x > 0 $
journal: j-J-COMPUT-PHYS
volume: 25
number: 2
pages: 199--204
month: oct
monthnumber: 10
year: 1977
CODEN: JCTPAH
DOI: https://doi.org/10.1016/0021-9991(77)90022-5
ISSN: 0021-9991 (print), 1090-2716 (electronic) OR 00219991 (print), 10902716 (electronic)
ISSNL: 0021-9991 OR 00219991
bibdate: Sun Jan 1 09:15:26 MST 2012
bibtimestamp: 2012.01.01 09:15:26 MST
URL: http://www.sciencedirect.com/science/article/pii/0021999177900225
fjournal: Journal of Computational Physics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00219991/
rawauthor: R. R. Sharma and Bahman Zohuri
rawtitle: A general method for an accurate evaluation of exponential integrals {$ E_1 (x), x > 0 $}
entry:
@Article{Sharma:1977:GMA,
  author =       "R. R. Sharma and Bahman Zohuri",
  title =        "A general method for an accurate evaluation of
                 exponential integrals {$ E_1 (x), x > 0 $}",
  journal =      j-J-COMPUT-PHYS,
  volume =       "25",
  number =       "2",
  pages =        "199--204",
  month =        oct,
  year =         "1977",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(77)90022-5",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Sun Jan 1 09:15:26 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1970.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0021999177900225",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}


bibtype: article
filename: elefunt.bib
label: Verma:1977:CSF
author: Arun Verma
title: Certain summation formulae for basic hypergeometric series
journal: j-CAN-MATH-BULL
volume: 20
pages: 369--376
year: 1977
CODEN: CMBUA3
DOI: https://doi.org/10.4153/CMB-1977-055-8
ISSN: 0008-4395 (print), 1496-4287 (electronic) OR 00084395 (print), 14964287 (electronic)
ISSNL: 0008-4395 OR 00084395
bibdate: Thu Sep 8 10:04:41 MDT 2011
bibtimestamp: 2011.09.08 10:04:41 MDT
fjournal: Canadian mathematical bulletin = Bulletin canadien de mathematiques
acknowledgement: ack-nhfb
journalURL: http://cms.math.ca/cmb/
rawauthor: Arun Verma
rawtitle: Certain summation formulae for basic hypergeometric series
bibsource:
http://cms.math.ca/cmb/v20/; https://www.math.utah.edu/pub/tex/bib/canmathbull.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Verma:1977:CSF,
  author =       "Arun Verma",
  title =        "Certain summation formulae for basic hypergeometric
                 series",
  journal =      j-CAN-MATH-BULL,
  volume =       "20",
  number =       "??",
  pages =        "369--376",
  month =        "????",
  year =         "1977",
  CODEN =        "CMBUA3",
  DOI =          "https://doi.org/10.4153/CMB-1977-055-8",
  ISSN =         "0008-4395 (print), 1496-4287 (electronic)",
  ISSN-L =       "0008-4395",
  bibdate =      "Thu Sep 8 10:04:41 MDT 2011",
  bibsource =    "http://cms.math.ca/cmb/v20/;
                 https://www.math.utah.edu/pub/tex/bib/canmathbull.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Canadian mathematical bulletin = Bulletin canadien de
                 math{\'e}matiques",
  journal-URL =  "http://cms.math.ca/cmb/",
}


bibtype: article
filename: elefunt.bib
label: Amos:1978:ECS
author: Donald E. Amos
journal: j-TOMS
volume: 4
number: 4
pages: 411--411
month: dec
monthnumber: 12
year: 1978
CODEN: ACMSCU
DOI: https://doi.org/10.1145/356502.356501
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Tue Aug 30 00:28:02 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.08.30 00:28:02 ???
note: See cite Amos:1977:ACS.
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Donald E. Amos
rawnote: See \cite{Amos:1977:ACS}.
title:
Erratum: ``Algorithm 511: CDC 6600 Subroutines IBESS and JBESS for Bessel Functions $ I_nu (x) $ and $ J_nu (x) $, $ x ge 0, nu ge 0 $ [S18]''

rawtitle:
Erratum: ``{Algorithm 511}: {CDC} 6600 Subroutines {IBESS} and {JBESS} for {Bessel} Functions {$ I_\nu (x) $} and {$ J_\nu (x) $}, {$ x \ge 0, \nu \ge 0 $} [{S18}]''

entry:
@Article{Amos:1978:ECS,
  author =       "Donald E. Amos",
  title =        "Erratum: ``{Algorithm 511}: {CDC} 6600 Subroutines
                 {IBESS} and {JBESS} for {Bessel} Functions {$ I_\nu (x)
                 $} and {$ J_\nu (x) $}, {$ x \ge 0, \nu \ge 0 $}
                 [{S18}]''",
  journal =      j-TOMS,
  volume =       "4",
  number =       "4",
  pages =        "411--411",
  month =        dec,
  year =         "1978",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356502.356501",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 30 00:28:02 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Amos:1977:ACS}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: article
filename: elefunt.bib
label: Andrews:1978:EFM
author: M. Andrews and S. F. McCormick and G. D. Taylor
title: Evaluation of Functions on Microcomputers: Square Root
journal: j-COMPUT-MATH-APPL
volume: 4
number: 4
pages: 359--367
year: 1978
CODEN: CMAPDK
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Thu Sep 15 18:40:29 1994
bibtimestamp: 1994.09.15 18:40:29 ???
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-nj
journalURL: http://www.sciencedirect.com/science/journal/08981221
rawauthor: M. Andrews and S. F. McCormick and G. D. Taylor
rawtitle: Evaluation of Functions on Microcomputers: Square Root
entry:
@Article{Andrews:1978:EFM,
  author =       "M. Andrews and S. F. McCormick and G. D. Taylor",
  title =        "Evaluation of Functions on Microcomputers: Square
                 Root",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "4",
  number =       "4",
  pages =        "359--367",
  year =         "1978",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Thu Sep 15 18:40:29 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
  xxmonth =      "(none)",
}


bibtype: article
filename: elefunt.bib
label: Andrews:1978:UEF
author: M. Andrews and T. Mraz
title: Unified elementary function generator
journal: j-MICROPROC-MICROSYS
volume: 2
number: 5
pages: 270--273
month: oct
monthnumber: 10
year: 1978
CODEN: MIMID5
ISSN: 0141-9331 (print), 1872-9436 (electronic) OR 01419331 (print), 18729436 (electronic)
ISSNL: 0141-9331 OR 01419331
bibdate: Thu Sep 1 10:15:39 1994
bibsource: garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.09.01 10:15:39 ???
fjournal: Microprocessors and Microsystems
acknowledgement: ack-nj
rawauthor: M. Andrews and T. Mraz
rawtitle: Unified elementary function generator
entry:
@Article{Andrews:1978:UEF,
  author =       "M. Andrews and T. Mraz",
  title =        "Unified elementary function generator",
  journal =      j-MICROPROC-MICROSYS,
  volume =       "2",
  number =       "5",
  pages =        "270--273",
  month =        oct,
  year =         "1978",
  CODEN =        "MIMID5",
  ISSN =         "0141-9331 (print), 1872-9436 (electronic)",
  ISSN-L =       "0141-9331",
  bibdate =      "Thu Sep 1 10:15:39 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nj,
  fjournal =     "Microprocessors and Microsystems",
}


bibtype: article
filename: elefunt.bib
label: Ardill:1978:SBF
author: R. W. B. Ardill and K. J. M. Moriarty
title: Spherical Bessel functions $ j_n $ and $ y_n $ of integer order and real argument
journal: j-COMP-PHYS-COMM
volume: 14
number: 3--4
pages: 261--265
month: may
monthnumber: 5
year: 1978
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/0010-4655(78)90019-X
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Thu Apr 24 10:35:27 2008
bibtimestamp: 2008.04.24 10:35:27 ???
URL: http://www.sciencedirect.com/science/article/pii/001046557890019X
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: R. W. B. Ardill and K. J. M. Moriarty
rawtitle: Spherical {Bessel} functions $ j_n $ and $ y_n $ of integer order and real argument
entry:
@Article{Ardill:1978:SBF,
  author =       "R. W. B. Ardill and K. J. M. Moriarty",
  title =        "Spherical {Bessel} functions $ j_n $ and $ y_n $ of
                 integer order and real argument",
  journal =      j-COMP-PHYS-COMM,
  volume =       "14",
  number =       "3--4",
  pages =        "261--265",
  month =        may # "\slash " # jun,
  year =         "1978",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(78)90019-X",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Thu Apr 24 10:35:27 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/001046557890019X",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}


bibtype: article
filename: elefunt.bib
label: Benton:1978:CZT
author: T. C. Benton and H. D. Knoble
title: Common Zeros of Two Bessel Functions
journal: j-MATH-COMPUT
volume: 32
number: 142
pages: 533--535
month: apr
monthnumber: 4
year: 1978
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
keywords: Bessel functions; common zeros; poles and zeros; positive zeros; zeros
acknowledgement: ack-nhfb
classcodes: C1110 (Algebra)
corpsource: Pennsylvania State Univ., University Park, PA, USA
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: T. C. Benton and H. D. Knoble
rawtitle: Common Zeros of Two {Bessel} Functions
entry:
@Article{Benton:1978:CZT,
  author =       "T. C. Benton and H. D. Knoble",
  title =        "Common Zeros of Two {Bessel} Functions",
  journal =      j-MATH-COMPUT,
  volume =       "32",
  number =       "142",
  pages =        "533--535",
  month =        apr,
  year =         "1978",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "C1110 (Algebra)",
  corpsource =   "Pennsylvania State Univ., University Park, PA, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Bessel functions; common zeros; poles and zeros;
                 positive zeros; zeros",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Blair:1978:RCA
author: J. M. Blair and C. A. Edwards and J. H. Johnson
title: Rational Chebyshev approximations for the Bickley functions $ K i_n(x) $
journal: j-MATH-COMPUT
volume: 32
number: 143
pages: 876--886
month: jul
monthnumber: 7
year: 1978
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
classcodes: C4130 (Interpolation and function approximation)
corpsource: Atomic Energy of Canada Ltd., Chalk River, Ont., Canada
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: J. M. Blair and C. A. Edwards and J. H. Johnson
rawtitle: Rational {Chebyshev} approximations for the {Bickley} functions {$ K i_n(x) $}
keywords:
approximation; Bessel functions; Bickley functions; Chebyshev approximation; Chebyshev approximations; function; recurrence; relation

remark:
Fullerton: Approximations accurate to 23 digits of repeated integrals of the Bessel function $ K_0 (x) $ for $ n = 1, 2, ldots , 10 $.

entry:
@Article{Blair:1978:RCA,
  author =       "J. M. Blair and C. A. Edwards and J. H. Johnson",
  title =        "Rational {Chebyshev} approximations for the {Bickley}
                 functions {$ K i_n(x) $}",
  journal =      j-MATH-COMPUT,
  volume =       "32",
  number =       "143",
  pages =        "876--886",
  month =        jul,
  year =         "1978",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "C4130 (Interpolation and function approximation)",
  corpsource =   "Atomic Energy of Canada Ltd., Chalk River, Ont.,
                 Canada",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "approximation; Bessel functions; Bickley functions;
                 Chebyshev approximation; Chebyshev approximations;
                 function; recurrence; relation",
  remark =       "Fullerton: Approximations accurate to 23 digits of
                 repeated integrals of the Bessel function $ K_0 (x) $
                 for $ n = 1, 2, \ldots {}, 10 $.",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Bowman:1978:ASS
author: K. O. Bowman and L. R. Shenton
title: Asymptotic series and Stieltjes continued fractions for a gamma function ratio
journal: j-J-COMPUT-APPL-MATH
volume: 4
number: 2
pages: 105--111
month: jun
monthnumber: 6
year: 1978
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 11:59:17 MST 2017
bibtimestamp: 2017.02.25 11:59:17 MST
URL: http://www.sciencedirect.com/science/article/pii/0771050X78900347
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: K. O. Bowman and L. R. Shenton
rawtitle: Asymptotic series and {Stieltjes} continued fractions for a gamma function ratio
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1970.bib

entry:
@Article{Bowman:1978:ASS,
  author =       "K. O. Bowman and L. R. Shenton",
  title =        "Asymptotic series and {Stieltjes} continued fractions
                 for a gamma function ratio",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "4",
  number =       "2",
  pages =        "105--111",
  month =        jun,
  year =         "1978",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 11:59:17 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1970.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0771050X78900347",
  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: Brezinski:1978:AAC
author: Claude Brezinski
publisher: Editions Technip
address: Paris, France
pages: xi + 392
year: 1978
ISBN: 2-7108-0341-0 (paperback) OR 2710803410 (paperback)
ISBN13: 978-2-7108-0341-6 (paperback) OR 9782710803416 (paperback)
bibdate: Thu Dec 1 10:20:23 MST 2011
bibsource: carmin.sudoc.abes.fr:210/ABES-Z39-PUBLIC; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2011.12.01 10:20:23 MST
keywords: convergence acceleration
language: French
acknowledgement: ack-nhfb
rawauthor: Claude Brezinski
title:
Algorithmes d'acceleration de la convergence: etude numerique. (French) [Algorithms for convergence acceleration: numerical study]

rawtitle:
Algorithmes d'acc{\'e}l{\'e}ration de la convergence: {\'e}tude num{\'e}rique. ({French}) [Algorithms for convergence acceleration: numerical study]

entry:
@Book{Brezinski:1978:AAC,
  author =       "Claude Brezinski",
  title =        "Algorithmes d'acc{\'e}l{\'e}ration de la convergence:
                 {\'e}tude num{\'e}rique. ({French}) [Algorithms for
                 convergence acceleration: numerical study]",
  publisher =    "{\'E}ditions Technip",
  address =      "Paris, France",
  pages =        "xi + 392",
  year =         "1978",
  ISBN =         "2-7108-0341-0 (paperback)",
  ISBN-13 =      "978-2-7108-0341-6 (paperback)",
  LCCN =         "????",
  bibdate =      "Thu Dec 1 10:20:23 MST 2011",
  bibsource =    "carmin.sudoc.abes.fr:210/ABES-Z39-PUBLIC;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  keywords =     "convergence acceleration",
  language =     "French",
}


bibtype: article
filename: elefunt.bib
label: Brezinski:1978:CAS
author: C. Brezinski
title: Convergence acceleration of some sequences by the $ epsilon $-algorithm
journal: j-NUM-MATH
volume: 29
number: 2
pages: 173--177
month: jan
monthnumber: 1
year: 1978
CODEN: NUMMA7
ISSN: 0029-599X (print), 0945-3245 (electronic) OR 0029599X (print), 09453245 (electronic)
ISSNL: 0029-599X OR 0029599X
bibdate: Mon May 26 11:49:34 MDT 1997
bibtimestamp: 1997.05.26 11:49:34 MDT
fjournal: Numerische Mathematik
acknowledgement: ack-nhfb
corpsource: UER d'IEEA-Informatique, Univ. de Lille I, Villeneuve d'Ascq, France
journalURL: http://link.springer.com/journal/211
treatment: T Theoretical or Mathematical
rawauthor: C. Brezinski
rawtitle: Convergence acceleration of some sequences by the $ \epsilon $-algorithm
keywords:
acceleration; converge; convergence acceleration; convergence of numerical methods; epsilon-algorithm; sequences

entry:
@Article{Brezinski:1978:CAS,
  author =       "C. Brezinski",
  title =        "Convergence acceleration of some sequences by the $
                 \epsilon $-algorithm",
  journal =      j-NUM-MATH,
  volume =       "29",
  number =       "2",
  pages =        "173--177",
  month =        jan,
  year =         "1978",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Mon May 26 11:49:34 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/nummath.bib",
  acknowledgement = ack-nhfb,
  classification = "C4140 (Linear algebra)",
  corpsource =   "UER d'IEEA-Informatique, Univ. de Lille I, Villeneuve
                 d'Ascq, France",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "acceleration; converge; convergence acceleration;
                 convergence of numerical methods; epsilon-algorithm;
                 sequences",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Brezinski:1978:SCA
author: C. Brezinski
title: Survey on convergence acceleration methods in numerical analysis
journal: j-MATH-STUDENT
volume: 46
number: 1
pages: 28--41 (1979)
year: 1978
CODEN: MTHSBH
ISSN: 0025-5742 OR 00255742
MRclass: 65B99
MRnumber: 698176 (84d:65003)
bibdate: Thu Dec 1 17:36:45 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2011.12.01 17:36:45 ???
fjournal: The Mathematics Student
keywords: convergence acceleration
acknowledgement: ack-nhfb
rawauthor: C. Brezinski
rawtitle: Survey on convergence acceleration methods in numerical analysis
entry:
@Article{Brezinski:1978:SCA,
  author =       "C. Brezinski",
  title =        "Survey on convergence acceleration methods in
                 numerical analysis",
  journal =      j-MATH-STUDENT,
  volume =       "46",
  number =       "1",
  pages =        "28--41 (1979)",
  year =         "1978",
  CODEN =        "MTHSBH",
  ISSN =         "0025-5742",
  MRclass =      "65B99",
  MRnumber =     "698176 (84d:65003)",
  bibdate =      "Thu Dec 1 17:36:45 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "The Mathematics Student",
  keywords =     "convergence acceleration",
}


bibtype: article
filename: elefunt.bib
label: Chin:1978:DAD
author: R. C. Y. Chin and G. W. Hedstrom
title: A dispersion analysis for difference schemes: tables of generalized Airy functions
journal: j-MATH-COMPUT
volume: 32
number: 144
pages: 1163--1170
month: oct
monthnumber: 10
year: 1978
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
classcodes: C4130 (Interpolation and function approximation); C4170 (Differential equations)
corpsource: Univ. of California, Lawrence Livermore Lab., Livermore, CA, USA
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: R. C. Y. Chin and G. W. Hedstrom
rawtitle: A dispersion analysis for difference schemes: tables of generalized {Airy} functions
keywords:
artificial viscosity; difference schemes; dispersion analysis; function approximation; functions; generalized Airy; linear hyperbolic equation

entry:
@Article{Chin:1978:DAD,
  author =       "R. C. Y. Chin and G. W. Hedstrom",
  title =        "A dispersion analysis for difference schemes: tables
                 of generalized {Airy} functions",
  journal =      j-MATH-COMPUT,
  volume =       "32",
  number =       "144",
  pages =        "1163--1170",
  month =        oct,
  year =         "1978",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "C4130 (Interpolation and function approximation);
                 C4170 (Differential equations)",
  corpsource =   "Univ. of California, Lawrence Livermore Lab.,
                 Livermore, CA, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "artificial viscosity; difference schemes; dispersion
                 analysis; function approximation; functions;
                 generalized Airy; linear hyperbolic equation",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Coleman:1978:RSN
author: John P. Coleman
title: Remark on ``Algorithm 49: Spherical Neumann Function''
journal: j-TOMS
volume: 4
number: 3
pages: 295--295
month: sep
monthnumber: 9
year: 1978
CODEN: ACMSCU
ISSN: 0098-3500 OR 00983500
bibdate: Sat Jul 05 16:48:40 1997
bibtimestamp: 1997.07.05 16:48:40 ???
note: See cite Herndon:1961:ASN.
keywords: Neumann functions; special functions
acknowledgement: ack-nhfb
rawauthor: John P. Coleman
rawnote: See \cite{Herndon:1961:ASN}.
rawtitle: Remark on {``Algorithm 49: Spherical Neumann Function''}
entry:
@Article{Coleman:1978:RSN,
  author =       "John P. Coleman",
  title =        "Remark on {``Algorithm 49: Spherical Neumann
                 Function''}",
  journal =      j-TOMS,
  volume =       "4",
  number =       "3",
  pages =        "295--295",
  month =        sep,
  year =         "1978",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500",
  bibdate =      "Sat Jul 05 16:48:40 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Herndon:1961:ASN}.",
  acknowledgement = ack-nhfb,
  keywords =     "Neumann functions; special functions",
}


bibtype: article
filename: elefunt.bib
label: DiDonato:1978:AR
author: A. R. DiDonato
title: An Approximation for $ int ^infty _x e^-t^2 / 2 t^p d t, x > 0, p $ Real
journal: j-MATH-COMPUT
volume: 32
number: 141
pages: 271--275
month: jan
monthnumber: 1
year: 1978
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
keywords: integral approximation; integration; numerical analysis
remark: Fullerton: Closely related to the complementary incomplete gamma function.
acknowledgement: ack-nhfb
classcodes: C4160 (Numerical integration and differentiation)
corpsource: Naval Surface Weapons Center, Dahlgren, VA, USA
journalURL: http://www.ams.org/mcom/
treatment: A Application; N New Development; T Theoretical or Mathematical
rawauthor: A. R. DiDonato
rawtitle: An Approximation for $ \int^\infty_x e^{-t^2 / 2} t^p d t, x > 0, p $ Real
entry:
@Article{DiDonato:1978:AR,
  author =       "A. R. DiDonato",
  title =        "An Approximation for $ \int^\infty_x e^{-t^2 / 2} t^p
                 d t, x > 0, p $ Real",
  journal =      j-MATH-COMPUT,
  volume =       "32",
  number =       "141",
  pages =        "271--275",
  month =        jan,
  year =         "1978",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "C4160 (Numerical integration and differentiation)",
  corpsource =   "Naval Surface Weapons Center, Dahlgren, VA, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "integral approximation; integration; numerical
                 analysis",
  remark =       "Fullerton: Closely related to the complementary
                 incomplete gamma function.",
  treatment =    "A Application; N New Development; T Theoretical or
                 Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Drezner:1978:CBN
author: Z. Drezner
title: Computation of the Bivariate Normal Integral
journal: j-MATH-COMPUT
volume: 32
number: 141
pages: 277--279
month: jan
monthnumber: 1
year: 1978
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
keywords: bivariate normal integral; computation; Gauss quadrature method; integration; numerical analysis
acknowledgement: ack-nhfb
corpsource: Faculty of Business, McMaster Univ., Hamilton, Ont., Canada
journalURL: http://www.ams.org/mcom/
treatment: A Application; T Theoretical or Mathematical
rawauthor: Z. Drezner
rawtitle: Computation of the Bivariate Normal Integral
classcodes:
B0290M (Numerical integration and differentiation); C4160 (Numerical integration and differentiation)

entry:
@Article{Drezner:1978:CBN,
  author =       "Z. Drezner",
  title =        "Computation of the Bivariate Normal Integral",
  journal =      j-MATH-COMPUT,
  volume =       "32",
  number =       "141",
  pages =        "277--279",
  month =        jan,
  year =         "1978",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "B0290M (Numerical integration and differentiation);
                 C4160 (Numerical integration and differentiation)",
  corpsource =   "Faculty of Business, McMaster Univ., Hamilton, Ont.,
                 Canada",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "bivariate normal integral; computation; Gauss
                 quadrature method; integration; numerical analysis",
  treatment =    "A Application; T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Dzjadyk:1978:CRP
author: V. K. Dzjadyk and L. I. Filozof
title: The convergence rate of Pade approximants for some elementary functions. (Russian)
journal: Mat. Sb. (N.S.)
volume: 107(149)
number: 3
pages: 347--363, 463
year: 1978
ISSN: 0368-8666 OR 03688666
MRclass: 41A21 (30E10 41A25)
MRnumber: 81b:41043
MRreviewer: B. D. Donevski
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
language: Russian
acknowledgement: ack-nhfb
rawauthor: V. K. Dzjadyk and L. {\=I}. F{\'\i}lozof
rawtitle: The convergence rate of {Pad{\'e}} approximants for some elementary functions. ({Russian})
entry:
@Article{Dzjadyk:1978:CRP,
  author =       "V. K. Dzjadyk and L. {\=I}. F{\'\i}lozof",
  title =        "The convergence rate of {Pad{\'e}} approximants for
                 some elementary functions. ({Russian})",
  journal =      "Mat. Sb. (N.S.)",
  volume =       "107(149)",
  number =       "3",
  pages =        "347--363, 463",
  year =         "1978",
  ISSN =         "0368-8666",
  MRclass =      "41A21 (30E10 41A25)",
  MRnumber =     "81b:41043",
  MRreviewer =   "B. D. Donevski",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  language =     "Russian",
}


bibtype: inproceedings
filename: elefunt.bib
label: Ercegovac:1978:LSR
author: Milos D. Ercegovac
title: An On-Line Square Rooting Algorithm
crossref: IEEE:1978:PSC
pages: 183--189
year: 1978
bibdate: Thu Nov 15 10:49:40 2007
bibtimestamp: 2007.11.15 10:49:40 ???
URL: http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Ercegovac.pdf
keywords: ARITH-4
acknowledgement: ack-nhfb
rawauthor: Milo{\v{s}} D. Ercegovac
rawtitle: An On-Line Square Rooting Algorithm
abstract:
An on-line algorithm for computing square roots in a radix 2, normalized floating-point number system with the redundant digit set $ - 1, 0, 1 $ is described. The algorithm has on-line delay of one and it is amenable for modular implementation. A systematic approach, used in deriving this algorithm, is presented in detail.

rawabstract:
An on-line algorithm for computing square roots in a radix 2, normalized floating-point number system with the redundant digit set $ \{ - 1, 0, 1 \} $ is described. The algorithm has on-line delay of one and it is amenable for modular implementation. A systematic approach, used in deriving this algorithm, is presented in detail.

entry:
@InProceedings{Ercegovac:1978:LSR,
  author =       "Milo{\v{s}} D. Ercegovac",
  title =        "An On-Line Square Rooting Algorithm",
  crossref =     "IEEE:1978:PSC",
  pages =        "183--189",
  year =         "1978",
  bibdate =      "Thu Nov 15 10:49:40 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Ercegovac.pdf",
  abstract =     "An on-line algorithm for computing square roots in a
                 radix 2, normalized floating-point number system with
                 the redundant digit set $ \{ - 1, 0, 1 \} $ is
                 described. The algorithm has on-line delay of one and
                 it is amenable for modular implementation. A systematic
                 approach, used in deriving this algorithm, is presented
                 in detail.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-4",
}


bibtype: book
filename: elefunt.bib
label: Feinsilver:1978:SFP
author: Philip J. (Philip Joel) Feinsilver
title: Special functions, probability semigroups, and Hamiltonian flows
volume: 696
publisher: pub-SV
address: pub-SV:adr
pages: vi + 112
year: 1978
ISBN: 0-387-09100-9 OR 0387091009
ISBN13: 978-0-387-09100-6 OR 9780387091006
LCCN: QA3 .L28 no. 696; QA273
bibdate: Sat Oct 30 19:22:05 MDT 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2010.10.30 19:22:05 MDT
series: Lecture notes in mathematics
subject: probabilities; semigroups; functions, special; Hamiltonian systems
acknowledgement: ack-nhfb
rawauthor: Philip J. (Philip Joel) Feinsilver
rawtitle: Special functions, probability semigroups, and {Hamiltonian} flows
entry:
@Book{Feinsilver:1978:SFP,
  author =       "Philip J. (Philip Joel) Feinsilver",
  title =        "Special functions, probability semigroups, and
                 {Hamiltonian} flows",
  volume =       "696",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "vi + 112",
  year =         "1978",
  ISBN =         "0-387-09100-9",
  ISBN-13 =      "978-0-387-09100-6",
  LCCN =         "QA3 .L28 no. 696; QA273",
  bibdate =      "Sat Oct 30 19:22:05 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Lecture notes in mathematics",
  acknowledgement = ack-nhfb,
  subject =      "probabilities; semigroups; functions, special;
                 Hamiltonian systems",
}


bibtype: inproceedings
filename: elefunt.bib
label: Frankowski:1978:RME
author: Krzysztof S. Frankowski
title: A Realistic Model for Error Estimates in the Evaluation of Elementary Functions
crossref: IEEE:1978:PSC
pages: 70--74
year: 1978
MRclass: 65G05 (65D20)
MRnumber: 80g:65050
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
acknowledgement: ack-nhfb
rawauthor: Krzysztof S. Frankowski
rawtitle: A Realistic Model for Error Estimates in the Evaluation of Elementary Functions
entry:
@InProceedings{Frankowski:1978:RME,
  author =       "Krzysztof S. Frankowski",
  title =        "A Realistic Model for Error Estimates in the
                 Evaluation of Elementary Functions",
  crossref =     "IEEE:1978:PSC",
  pages =        "70--74",
  year =         "1978",
  MRclass =      "65G05 (65D20)",
  MRnumber =     "80g:65050",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Gautschi:1978:CMB
author: Walter Gautschi and Josef Slavik
title: On the computation of modified Bessel function ratios
journal: j-MATH-COMPUT
volume: 32
number: 143
pages: 865--875
month: jul
monthnumber: 7
year: 1978
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
classcodes: C1120 (Mathematical analysis); C4130 (Interpolation and function approximation)
corpsource: Dept. of Computer Sci., Purdue Univ., Lafayette, IN, USA
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: Walter Gautschi and Josef Slavik
rawtitle: On the computation of modified {Bessel} function ratios
keywords:
Bessel; Bessel functions; continued fraction; fraction; function approximation; functions; Gauss' continued; modified Bessel function ratios; Perron's continued fraction

entry:
@Article{Gautschi:1978:CMB,
  author =       "Walter Gautschi and Josef Slavik",
  title =        "On the computation of modified {Bessel} function
                 ratios",
  journal =      j-MATH-COMPUT,
  volume =       "32",
  number =       "143",
  pages =        "865--875",
  month =        jul,
  year =         "1978",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "C1120 (Mathematical analysis); C4130 (Interpolation
                 and function approximation)",
  corpsource =   "Dept. of Computer Sci., Purdue Univ., Lafayette, IN,
                 USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Bessel; Bessel functions; continued fraction;
                 fraction; function approximation; functions; Gauss'
                 continued; modified Bessel function ratios; Perron's
                 continued fraction",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Gustafson:1978:ATC
author: S.-AA . Gustafson
title: Algorithm $ 38 $. Two computer codes for convergence acceleration
journal: j-COMPUTING
volume: 21
number: 1
pages: 87--91
year: 1978
CODEN: CMPTA2
ISSN: 0010-485X (print), 1436-5057 (electronic) OR 0010485X (print), 14365057 (electronic)
ISSNL: 0010-485X OR 0010485X
MRclass: 65B10
MRnumber: 83a:65005
bibdate: Tue Jan 2 17:40:53 MST 2001
bibtimestamp: 2001.01.02 17:40:53 MST
fjournal: Computing
keywords: codes, symbolic; convergence acceleration; power series sum
acknowledgement: ack-nhfb
affiliation: Australian Nat. Univ., Canberra, ACT, Australia
journalURL: http://link.springer.com/journal/607
journalabr: Computing (Vienna/New York)
rawauthor: S.-{\AA}. Gustafson
rawtitle: Algorithm $ 38 $. {Two} computer codes for convergence acceleration
bibsource:
Compendex database; http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; INSPEC Axiom database (1968--date); MathSciNet database

entry:
@Article{Gustafson:1978:ATC,
  author =       "S.-{\AA}. Gustafson",
  title =        "Algorithm $ 38 $. {Two} computer codes for convergence
                 acceleration",
  journal =      j-COMPUTING,
  volume =       "21",
  number =       "1",
  pages =        "87--91",
  year =         "1978",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  MRclass =      "65B10",
  MRnumber =     "83a:65005",
  bibdate =      "Tue Jan 2 17:40:53 MST 2001",
  bibsource =    "Compendex database;
                 http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 INSPEC Axiom database (1968--date); MathSciNet
                 database",
  acknowledgement = ack-nhfb,
  affiliation =  "Australian Nat. Univ., Canberra, ACT, Australia",
  classification = "723; C4140",
  description =  "convergence of numerical methods",
  fjournal =     "Computing",
  journal-URL =  "http://link.springer.com/journal/607",
  journalabr =   "Computing (Vienna/New York)",
  keywords =     "codes, symbolic; convergence acceleration; power
                 series sum",
}


bibtype: article
filename: elefunt.bib
label: Gustafson:1978:CAG
author: S.-AA . Gustafson
title: Convergence acceleration on a general class of power series
journal: j-COMPUTING
volume: 21
number: 1
pages: 53--69
year: 1978
CODEN: CMPTA2
ISSN: 0010-485X (print), 1436-5057 (electronic) OR 0010485X (print), 14365057 (electronic)
ISSNL: 0010-485X OR 0010485X
MRclass: 65B10 (40A05)
MRnumber: 83m:65005
MRreviewer: A. M. Cohen
bibdate: Tue Jan 2 17:40:53 MST 2001
bibtimestamp: 2001.01.02 17:40:53 MST
fjournal: Computing
keywords: algorithms; convergence acceleration; power series
acknowledgement: ack-nhfb
affiliation: Australian Nat. Univ., Canberra, ACT, Australia
journalURL: http://link.springer.com/journal/607
rawauthor: S.-{\AA}. Gustafson
rawtitle: Convergence acceleration on a general class of power series
bibsource:
http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; INSPEC Axiom database (1968--date); MathSciNet database

entry:
@Article{Gustafson:1978:CAG,
  author =       "S.-{\AA}. Gustafson",
  title =        "Convergence acceleration on a general class of power
                 series",
  journal =      j-COMPUTING,
  volume =       "21",
  number =       "1",
  pages =        "53--69",
  year =         "1978",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  MRclass =      "65B10 (40A05)",
  MRnumber =     "83m:65005",
  MRreviewer =   "A. M. Cohen",
  bibdate =      "Tue Jan 2 17:40:53 MST 2001",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 INSPEC Axiom database (1968--date); MathSciNet
                 database",
  acknowledgement = ack-nhfb,
  affiliation =  "Australian Nat. Univ., Canberra, ACT, Australia",
  classification = "C4120",
  description =  "convergence of numerical methods; function
                 evaluation",
  fjournal =     "Computing",
  journal-URL =  "http://link.springer.com/journal/607",
  keywords =     "algorithms; convergence acceleration; power series",
}


bibtype: article
filename: elefunt.bib
label: Hamaker:1978:MAC
author: Hugo C. Hamaker
title: Miscellanea: Approximating the Cumulative Normal Distribution and its Inverse
journal: j-APPL-STAT
volume: 27
number: 1
pages: 76--77
month: jan
monthnumber: 1
year: 1978
CODEN: APSTAG
ISSN: 0035-9254 (print), 1467-9876 (electronic) OR 00359254 (print), 14679876 (electronic)
ISSNL: 0035-9254 OR 00359254
bibdate: Sat Apr 21 10:22:12 MDT 2001
bibtimestamp: 2001.04.21 10:22:12 MDT
fjournal: Applied Statistics
acknowledgement: ack-nhfb
journalURL: http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-9876/issues
rawauthor: Hugo C. Hamaker
rawtitle: Miscellanea: Approximating the Cumulative Normal Distribution and its Inverse
bibsource:
https://www.math.utah.edu/pub/tex/bib/as1970.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database

entry:
@Article{Hamaker:1978:MAC,
  author =       "Hugo C. Hamaker",
  title =        "Miscellanea: Approximating the Cumulative Normal
                 Distribution and its Inverse",
  journal =      j-APPL-STAT,
  volume =       "27",
  number =       "1",
  pages =        "76--77",
  month =        jan,
  year =         "1978",
  CODEN =        "APSTAG",
  ISSN =         "0035-9254 (print), 1467-9876 (electronic)",
  ISSN-L =       "0035-9254",
  bibdate =      "Sat Apr 21 10:22:12 MDT 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/as1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Statistics",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-9876/issues",
}


bibtype: inproceedings
filename: elefunt.bib
label: Hull:1978:DFP
author: T. E. Hull
title: Desirable Floating-Point Arithmetic and Elementary Functions for Numerical Computation
crossref: IEEE:1978:PSC
pages: 63--69
year: 1978
bibdate: Thu Sep 01 12:14:34 1994
bibsource: garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.09.01 12:14:34 ???
acknowledgement: ack-nj
rawauthor: T. E. Hull
rawtitle: Desirable Floating-Point Arithmetic and Elementary Functions for Numerical Computation
entry:
@InProceedings{Hull:1978:DFP,
  author =       "T. E. Hull",
  title =        "Desirable Floating-Point Arithmetic and Elementary
                 Functions for Numerical Computation",
  crossref =     "IEEE:1978:PSC",
  pages =        "63--69",
  year =         "1978",
  bibdate =      "Thu Sep 01 12:14:34 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nj,
}


bibtype: article
filename: elefunt.bib
label: Katholi:1978:CVP
author: Charles R. Katholi
title: On the computation of values of the psi function from rapidly converging power series expansions
journal: j-J-STAT-COMPUT-SIMUL
volume: 8
number: 1
pages: 25--42
year: 1978
CODEN: JSCSAJ
DOI: https://doi.org/10.1080/00949657808810245
ISSNL: 0094-9655 OR 00949655
bibdate: Tue Apr 22 09:10:43 MDT 2014
bibtimestamp: 2014.04.22 09:10:43 MDT
fjournal: Journal of Statistical Computation and Simulation
acknowledgement: ack-nhfb
journalURL: http://www.tandfonline.com/loi/gscs20
rawauthor: Charles R. Katholi
rawtitle: On the computation of values of the psi function from rapidly converging power series expansions
ISSN:
0094-9655 (print), 1026-7778 (electronic), 1563-5163 OR 00949655 (print), 10267778 (electronic), 15635163

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

entry:
@Article{Katholi:1978:CVP,
  author =       "Charles R. Katholi",
  title =        "On the computation of values of the psi function from
                 rapidly converging power series expansions",
  journal =      j-J-STAT-COMPUT-SIMUL,
  volume =       "8",
  number =       "1",
  pages =        "25--42",
  year =         "1978",
  CODEN =        "JSCSAJ",
  DOI =          "https://doi.org/10.1080/00949657808810245",
  ISSN =         "0094-9655 (print), 1026-7778 (electronic), 1563-5163",
  ISSN-L =       "0094-9655",
  bibdate =      "Tue Apr 22 09:10:43 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jstatcomputsimul.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Statistical Computation and Simulation",
  journal-URL =  "http://www.tandfonline.com/loi/gscs20",
}


bibtype: article
filename: elefunt.bib
label: Ling:1978:EWZ
author: Chin-Bing Ling
title: Evaluation of Weierstrass Zeta Functions
journal: j-SIAM-REVIEW
volume: 20
number: 1
pages: 183--183
year: 1978
CODEN: SIREAD
DOI: https://doi.org/10.1137/1020017
ISSN: 0036-1445 (print), 1095-7200 (electronic) OR 00361445 (print), 10957200 (electronic)
ISSNL: 0036-1445 OR 00361445
bibdate: Sat Mar 29 09:52:48 MDT 2014
bibtimestamp: 2014.03.29 09:52:48 MDT
fjournal: SIAM Review
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sirev
onlinedate: January 1978
rawauthor: Chin-Bing Ling
rawtitle: Evaluation of {Weierstrass} Zeta Functions
bibsource:
http://epubs.siam.org/toc/siread/20/1; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib

entry:
@Article{Ling:1978:EWZ,
  author =       "Chin-Bing Ling",
  title =        "Evaluation of {Weierstrass} Zeta Functions",
  journal =      j-SIAM-REVIEW,
  volume =       "20",
  number =       "1",
  pages =        "183--183",
  month =        "????",
  year =         "1978",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/1020017",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Sat Mar 29 09:52:48 MDT 2014",
  bibsource =    "http://epubs.siam.org/toc/siread/20/1;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  onlinedate =   "January 1978",
}


bibtype: article
filename: elefunt.bib
label: Morita:1978:CCE
author: T. Morita
title: Calculation of the complete elliptic integrals with complex modulus
journal: j-NUM-MATH
volume: 29
number: 2
pages: 233--236
month: jan
monthnumber: 1
year: 1978
CODEN: NUMMA7
ISSN: 0029-599X (print), 0945-3245 (electronic) OR 0029599X (print), 09453245 (electronic)
ISSNL: 0029-599X OR 0029599X
bibdate: Mon May 26 11:49:34 MDT 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.05.26 11:49:34 MDT
fjournal: Numerische Mathematik
keywords: complete elliptic integrals; complex modulus; integration
remark: Fullerton: Addendum to a paper by Morita and Horiguchi.
acknowledgement: ack-nhfb
corpsource: Dept. of Appl. Sci., Faculty of Engng., Tohoku Univ., Sendai, Japan
journalURL: http://link.springer.com/journal/211
treatment: T Theoretical or Mathematical
rawauthor: T. Morita
rawtitle: Calculation of the complete elliptic integrals with complex modulus
entry:
@Article{Morita:1978:CCE,
  author =       "T. Morita",
  title =        "Calculation of the complete elliptic integrals with
                 complex modulus",
  journal =      j-NUM-MATH,
  volume =       "29",
  number =       "2",
  pages =        "233--236",
  month =        jan,
  year =         "1978",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Mon May 26 11:49:34 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classification = "C4160 (Numerical integration and differentiation)",
  corpsource =   "Dept. of Appl. Sci., Faculty of Engng., Tohoku Univ.,
                 Sendai, Japan",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "complete elliptic integrals; complex modulus;
                 integration",
  remark =       "Fullerton: Addendum to a paper by Morita and
                 Horiguchi.",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Pexton:1978:RTT
author: Robert L. Pexton and Arno D. Steiger
title: Roots of two transcendental equations as functions of a continuous real parameter
journal: j-MATH-COMPUT
volume: 32
number: 142
pages: 511--518
month: apr
monthnumber: 4
year: 1978
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
keywords: continuous real parameter; equations; roots; spherical Bessel functions; transcendental equations
acknowledgement: ack-nhfb
classcodes: C1110 (Algebra)
corpsource: Lawrence Livermore Lab., Univ. of California, Livermore, CA, USA
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: Robert L. Pexton and Arno D. Steiger
rawtitle: Roots of two transcendental equations as functions of a continuous real parameter
entry:
@Article{Pexton:1978:RTT,
  author =       "Robert L. Pexton and Arno D. Steiger",
  title =        "Roots of two transcendental equations as functions of
                 a continuous real parameter",
  journal =      j-MATH-COMPUT,
  volume =       "32",
  number =       "142",
  pages =        "511--518",
  month =        apr,
  year =         "1978",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "C1110 (Algebra)",
  corpsource =   "Lawrence Livermore Lab., Univ. of California,
                 Livermore, CA, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "continuous real parameter; equations; roots; spherical
                 Bessel functions; transcendental equations",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Preston:1978:NAT
author: F. S. Preston
title: A New Algorithm for the Tangent
journal: j-IEEE-TRANS-COMPUT
volume: C-27
number: 2
pages: 167--167
month: feb
monthnumber: 2
year: 1978
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1978.1675052
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Mon Jul 11 08:13:26 MDT 2011
bibtimestamp: 2011.07.11 08:13:26 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675052
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nj
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: F. S. Preston
rawtitle: A New Algorithm for the Tangent
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib

abstract:
A new mathematical algorithm has been developed for the tangent. The form of the equation guarantees that the error is zero at $ 0^circ $, $ 45^circ $, and $ 90^circ $ corresponding to tangents of $0$, $1$, and infinity. With only one constant the error is brought to zero at two more points and the maximum error is less than one part in $ 3000 $. By adding a second constant, the error is reduced to less than one in $ 720 000 $. Further terms improve the accuracy geometrically.

rawabstract:
A new mathematical algorithm has been developed for the tangent. The form of the equation guarantees that the error is zero at $ 0^\circ $, $ 45^\circ $, and $ 90^\circ $ corresponding to tangents of $0$, $1$, and infinity. With only one constant the error is brought to zero at two more points and the maximum error is less than one part in $ 3000 $. By adding a second constant, the error is reduced to less than one in $ 720 \, 000 $. Further terms improve the accuracy geometrically.

entry:
@Article{Preston:1978:NAT,
  author =       "F. S. Preston",
  title =        "A New Algorithm for the Tangent",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-27",
  number =       "2",
  pages =        "167--167",
  month =        feb,
  year =         "1978",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1978.1675052",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 11 08:13:26 MDT 2011",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 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=1675052",
  abstract =     "A new mathematical algorithm has been developed for
                 the tangent. The form of the equation guarantees that
                 the error is zero at $ 0^\circ $, $ 45^\circ $, and $
                 90^\circ $ corresponding to tangents of $0$, $1$, and
                 infinity. With only one constant the error is brought
                 to zero at two more points and the maximum error is
                 less than one part in $ 3000 $. By adding a second
                 constant, the error is reduced to less than one in $
                 720 \, 000 $. Further terms improve the accuracy
                 geometrically.",
  acknowledgement = ack-nj # "\slash " # ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: elefunt.bib
label: Schindler:1978:GCG
author: Susan Schindler and R. Mirman
title: Generation of the Clebsch-Gordan coefficients for $ S_n $
journal: j-COMP-PHYS-COMM
volume: 15
number: 1--2
pages: 131--145
month: sep
monthnumber: 9
year: 1978
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/0010-4655(78)90087-5
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Sun Oct 31 09:20:58 2010
bibtimestamp: 2010.10.31 09:20:58 ???
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: Susan Schindler and R. Mirman
rawtitle: Generation of the {Clebsch-Gordan} coefficients for {$ S_n $}
entry:
@Article{Schindler:1978:GCG,
  author =       "Susan Schindler and R. Mirman",
  title =        "Generation of the {Clebsch-Gordan} coefficients for {$
                 S_n $}",
  journal =      j-COMP-PHYS-COMM,
  volume =       "15",
  number =       "1--2",
  pages =        "131--145",
  month =        sep,
  year =         "1978",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(78)90087-5",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Sun Oct 31 09:20:58 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}


bibtype: article
filename: elefunt.bib
label: Schmidt:1978:EI
author: Paul W. Schmidt
journal: j-MATH-COMPUT
volume: 32
number: 141
pages: 265--269
month: jan
monthnumber: 1
year: 1978
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
corpsource: Phys. Dept., Univ. of Missouri, Columbia, MO, USA
journalURL: http://www.ams.org/mcom/
treatment: A Application; T Theoretical or Mathematical
rawauthor: Paul W. Schmidt
title:
Evaluation of the Integral $ int ^infty _0 frac t^2 alpha - 1 J_nu (x sqrt 1 + t^2)(1 + t^2)^alpha + beta - 1 d t $

keywords:
cylinder diameter distribution; first kind Bessel function; integral evaluation; integration; long circular; neutron scattering data; numerical analysis; power series expansions; recurrence; relations

rawtitle:
Evaluation of the Integral $ \int^\infty_0 \frac {t^{2 \alpha - 1} J_\nu (x \sqrt {1 + t^2})(1 + t^2)^{\alpha + \beta - 1}} d t $

entry:
@Article{Schmidt:1978:EI,
  author =       "Paul W. Schmidt",
  title =        "Evaluation of the Integral $ \int^\infty_0 \frac {t^{2
                 \alpha - 1} J_\nu (x \sqrt {1 + t^2})(1 + t^2)^{\alpha
                 + \beta - 1}} d t $",
  journal =      j-MATH-COMPUT,
  volume =       "32",
  number =       "141",
  pages =        "265--269",
  month =        jan,
  year =         "1978",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "B0290M (Numerical integration and differentiation);
                 C4160 (Numerical integration and differentiation)",
  corpsource =   "Phys. Dept., Univ. of Missouri, Columbia, MO, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "cylinder diameter distribution; first kind Bessel
                 function; integral evaluation; integration; long
                 circular; neutron scattering data; numerical analysis;
                 power series expansions; recurrence; relations",
  treatment =    "A Application; T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Schoene:1978:RMI
author: Andrew Y. Schoene
title: Remark on ``Algorithm 435: Modified Incomplete Gamma Function [S14]''
journal: j-TOMS
volume: 4
number: 3
pages: 296--304
month: sep
monthnumber: 9
year: 1978
CODEN: ACMSCU
DOI: https://doi.org/10.1145/355791.355803
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Tue Aug 30 00:28:02 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.08.30 00:28:02 ???
note: See cite Fullerton:1972:MIG.
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Andrew Y. Schoene
rawnote: See \cite{Fullerton:1972:MIG}.
rawtitle: Remark on ``{Algorithm 435}: Modified Incomplete Gamma Function [{S14}]''
entry:
@Article{Schoene:1978:RMI,
  author =       "Andrew Y. Schoene",
  title =        "Remark on ``{Algorithm 435}: Modified Incomplete Gamma
                 Function [{S14}]''",
  journal =      j-TOMS,
  volume =       "4",
  number =       "3",
  pages =        "296--304",
  month =        sep,
  year =         "1978",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355791.355803",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 30 00:28:02 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Fullerton:1972:MIG}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: article
filename: elefunt.bib
label: Schonfelder:1978:CEE
author: J. L. Schonfelder
title: Chebyshev expansions for the error and related functions
journal: j-MATH-COMPUT
volume: 32
number: 144
pages: 1232--1240
month: oct
monthnumber: 10
year: 1978
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
classcodes: C4110 (Error analysis in numerical methods); C4130 (Interpolation and function approximation)
corpsource: Computer Centre, Univ. of Birmingham, Birmingham, UK
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: J. L. Schonfelder
rawtitle: {Chebyshev} expansions for the error and related functions
keywords:
approximations; Chebyshev approximation; Chebyshev expansions; error analysis; error function; mappings; NAG library

remark:
Fullerton: Approximations for $ erf (x) $, $ erfc (x) $, and probability functions $ P(x) $, $ Q(x) $ with accuracy down to $ 10^-30 $.

entry:
@Article{Schonfelder:1978:CEE,
  author =       "J. L. Schonfelder",
  title =        "{Chebyshev} expansions for the error and related
                 functions",
  journal =      j-MATH-COMPUT,
  volume =       "32",
  number =       "144",
  pages =        "1232--1240",
  month =        oct,
  year =         "1978",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "C4110 (Error analysis in numerical methods); C4130
                 (Interpolation and function approximation)",
  corpsource =   "Computer Centre, Univ. of Birmingham, Birmingham, UK",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "approximations; Chebyshev approximation; Chebyshev
                 expansions; error analysis; error function; mappings;
                 NAG library",
  remark =       "Fullerton: Approximations for $ \erf (x) $, $ \erfc
                 (x) $, and probability functions $ P(x) $, $ Q(x) $
                 with accuracy down to $ 10^{-30} $.",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Skovgaard:1978:RCE
author: Ove Skovgaard
title: Remark on ``Algorithm 149: Complete Elliptic Integral [S21]''
journal: j-TOMS
volume: 4
number: 1
pages: 95--95
month: mar
monthnumber: 3
year: 1978
CODEN: ACMSCU
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Tue Feb 06 05:28:13 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1996.02.06 05:28:13 ???
note: See cite Merner:1962:AAC.
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Ove Skovgaard
rawnote: See \cite{Merner:1962:AAC}.
rawtitle: Remark on ``{Algorithm 149: Complete Elliptic Integral [S21]}''
entry:
@Article{Skovgaard:1978:RCE,
  author =       "Ove Skovgaard",
  title =        "Remark on ``{Algorithm 149: Complete Elliptic Integral
                 [S21]}''",
  journal =      j-TOMS,
  volume =       "4",
  number =       "1",
  pages =        "95--95",
  month =        mar,
  year =         "1978",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Feb 06 05:28:13 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Merner:1962:AAC}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: article
filename: elefunt.bib
label: Slepian:1978:PSW
author: D. Slepian
title: Prolate Spheroidal Wave Functions, Fourier Analysis, and Uncertainty --- V: The Discrete Case
journal: j-BELL-SYST-TECH-J
volume: 57
number: 5
pages: 1371--1430
month: may
monthnumber: 5
year: 1978
CODEN: BSTJAN
ISSN: 0005-8580 OR 00058580
bibdate: Tue Nov 9 11:15:56 MST 2010
bibtimestamp: 2010.11.09 11:15:56 MST
URL: http://bstj.bell-labs.com/BSTJ/images/Vol57/bstj57-5-1371.pdf
fjournal: The Bell System Technical Journal
acknowledgement: ack-nhfb
journalURL: http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/
rawauthor: D. Slepian
rawtitle: Prolate Spheroidal Wave Functions, {Fourier} Analysis, and Uncertainty --- {V}: The Discrete Case
bibsource:
http://bstj.bell-labs.com/oldfiles/year.1978/BSTJ.1978.5705.html; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Slepian:1978:PSW,
  author =       "D. Slepian",
  title =        "Prolate Spheroidal Wave Functions, {Fourier} Analysis,
                 and Uncertainty --- {V}: The Discrete Case",
  journal =      j-BELL-SYST-TECH-J,
  volume =       "57",
  number =       "5",
  pages =        "1371--1430",
  month =        may # "--" # jun,
  year =         "1978",
  CODEN =        "BSTJAN",
  ISSN =         "0005-8580",
  bibdate =      "Tue Nov 9 11:15:56 MST 2010",
  bibsource =    "http://bstj.bell-labs.com/oldfiles/year.1978/BSTJ.1978.5705.html;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://bstj.bell-labs.com/BSTJ/images/Vol57/bstj57-5-1371.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "The Bell System Technical Journal",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/",
}


bibtype: article
filename: elefunt.bib
label: Temme:1978:UAE
author: N. M. Temme
title: Uniform asymptotic expansions of confluent hypergeometric functions
journal: j-J-INST-MATH-APPL
volume: 22
number: 2
pages: 215--223
year: 1978
CODEN: JMTAA8
ISSN: 0020-2932 OR 00202932
MRclass: 33A30
MRnumber: 80a:33004
MRreviewer: F. W. J. Olver
bibdate: Fri Apr 5 05:48:27 MST 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; MathSciNet database
bibtimestamp: 2002.04.05 05:48:27 MST
fjournal: Journal of the Institute of Mathematics and its Applications
acknowledgement: ack-nhfb
journalURL: http://imamat.oxfordjournals.org/content/by/year
rawauthor: N. M. Temme
rawtitle: Uniform asymptotic expansions of confluent hypergeometric functions
entry:
@Article{Temme:1978:UAE,
  author =       "N. M. Temme",
  title =        "Uniform asymptotic expansions of confluent
                 hypergeometric functions",
  journal =      j-J-INST-MATH-APPL,
  volume =       "22",
  number =       "2",
  pages =        "215--223",
  year =         "1978",
  CODEN =        "JMTAA8",
  ISSN =         "0020-2932",
  MRclass =      "33A30",
  MRnumber =     "80a:33004",
  MRreviewer =   "F. W. J. Olver",
  bibdate =      "Fri Apr 5 05:48:27 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 MathSciNet database",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the Institute of Mathematics and its
                 Applications",
  journal-URL =  "http://imamat.oxfordjournals.org/content/by/year",
}


bibtype: article
filename: elefunt.bib
label: Alt:1979:SRD
author: H. Alt
title: Square Rooting Is as Difficult as Multiplication
journal: j-COMPUTING
volume: 21
number: 3
pages: 221--232
month: sep
monthnumber: 9
year: 1979
CODEN: CMPTA2
ISSN: 0010-485X (print), 1436-5057 (electronic) OR 0010485X (print), 14365057 (electronic)
ISSNL: 0010-485X OR 0010485X
MRclass: 68C25
MRnumber: 82m:68081
bibdate: Tue Jan 2 17:40:54 MST 2001
bibtimestamp: 2001.01.02 17:40:54 MST
fjournal: Computing
keywords: algorithm; computer programming; square rooting
acknowledgement: ack-nj
affiliation: Math. & Information, Univ. of Saarlandes, Saarbrucken, West Germany
journalURL: http://link.springer.com/journal/607
journalabr: Computing (Vienna/New York)
rawauthor: H. Alt
rawtitle: Square Rooting Is as Difficult as Multiplication
bibsource:
Compendex database; garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt; https://www.math.utah.edu/pub/tex/bib/computing.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; INSPEC Axiom database (1968--date); MathSciNet database

entry:
@Article{Alt:1979:SRD,
  author =       "H. Alt",
  title =        "Square Rooting Is as Difficult as Multiplication",
  journal =      j-COMPUTING,
  volume =       "21",
  number =       "3",
  pages =        "221--232",
  month =        sep,
  year =         "1979",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  MRclass =      "68C25",
  MRnumber =     "82m:68081",
  bibdate =      "Tue Jan 2 17:40:54 MST 2001",
  bibsource =    "Compendex database;
                 garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/computing.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 INSPEC Axiom database (1968--date); MathSciNet
                 database",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  affiliation =  "Math. \& Information, Univ. of Saarlandes,
                 Saarbrucken, West Germany",
  classification = "723; C5230",
  description =  "digital arithmetic",
  fjournal =     "Computing",
  journal-URL =  "http://link.springer.com/journal/607",
  journalabr =   "Computing (Vienna/New York)",
  keywords =     "algorithm; computer programming; square rooting",
}


bibtype: article
filename: elefunt.bib
label: Ardill:1979:ABF
author: R. W. B. Ardill and K. J. M. Moriarty
journal: j-COMP-PHYS-COMM
volume: 17
number: 3
pages: 321--336
month: jun
monthnumber: 6
year: 1979
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/0010-4655(79)90060-2
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Thu Apr 24 10:35:27 2008
bibtimestamp: 2008.04.24 10:35:27 ???
fjournal: Computer Physics Communications
remark: Fullerton: Description of a program with accuracy about $ 10^-10 $.
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: R. W. B. Ardill and K. J. M. Moriarty
title:
Accurate Bessel functions $ J_n(z) $, $ Y_n(z) $, $ H_n^(1)(z) $ and $ H_n^(2)(z) $ of integer order and complex argument

rawtitle:
Accurate {Bessel} functions {$ J_n(z) $}, {$ Y_n(z) $}, {$ H_n^{(1)}(z) $} and {$ H_n^{(2)}(z) $} of integer order and complex argument

entry:
@Article{Ardill:1979:ABF,
  author =       "R. W. B. Ardill and K. J. M. Moriarty",
  title =        "Accurate {Bessel} functions {$ J_n(z) $}, {$ Y_n(z)
                 $}, {$ H_n^{(1)}(z) $} and {$ H_n^{(2)}(z) $} of
                 integer order and complex argument",
  journal =      j-COMP-PHYS-COMM,
  volume =       "17",
  number =       "3",
  pages =        "321--336",
  month =        jun,
  year =         "1979",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(79)90060-2",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Thu Apr 24 10:35:27 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
  remark =       "Fullerton: Description of a program with accuracy
                 about $ 10^{-10} $.",
}


bibtype: article
filename: elefunt.bib
label: Atkins:1979:FSC
author: D. E. Atkins
title: Fourth Symposium on Computer Arithmetic: crunching with quality and LSI
journal: j-COMPUTER
volume: 12
number: 4
pages: 94--97
month: apr
monthnumber: 4
year: 1979
CODEN: CPTRB4
ISSN: 0018-9162 (print), 1558-0814 (electronic) OR 00189162 (print), 15580814 (electronic)
ISSNL: 0018-9162 OR 00189162
bibdate: Thu Dec 12 07:20:54 MST 1996
bibsource: Compendex database; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1996.12.12 07:20:54 MST
fjournal: Computer
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2
journalabr: Computer
rawauthor: D. E. Atkins
rawtitle: {Fourth Symposium on Computer Arithmetic}: crunching with quality and {LSI}
abstract:
Computer arithmetic problems --- faster computation rates and more efficient representations of real numbers --- are considered in the paper. Floating-point arithmetic standardization, novel implementation of basic arithmetic operators, evaluation of elementary functions --- these are the main considerations of the conference review.

keywords:
computer arithmetic; computer systems, digital; data processing --- data description; mathematical techniques --- digital arithmetic

rawabstract:
Computer arithmetic problems --- faster computation rates and more efficient representations of real numbers --- are considered in the paper. Floating-point arithmetic standardization, novel implementation of basic arithmetic operators, evaluation of elementary functions --- these are the main considerations of the conference review.

entry:
@Article{Atkins:1979:FSC,
  author =       "D. E. Atkins",
  title =        "{Fourth Symposium on Computer Arithmetic}: crunching
                 with quality and {LSI}",
  journal =      j-COMPUTER,
  volume =       "12",
  number =       "4",
  pages =        "94--97",
  month =        apr,
  year =         "1979",
  CODEN =        "CPTRB4",
  ISSN =         "0018-9162 (print), 1558-0814 (electronic)",
  ISSN-L =       "0018-9162",
  bibdate =      "Thu Dec 12 07:20:54 MST 1996",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "Computer arithmetic problems --- faster computation
                 rates and more efficient representations of real
                 numbers --- are considered in the paper. Floating-point
                 arithmetic standardization, novel implementation of
                 basic arithmetic operators, evaluation of elementary
                 functions --- these are the main considerations of the
                 conference review.",
  acknowledgement = ack-nhfb,
  classification = "722; 723",
  fjournal =     "Computer",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
  journalabr =   "Computer",
  keywords =     "computer arithmetic; computer systems, digital; data
                 processing --- data description; mathematical
                 techniques --- digital arithmetic",
}


bibtype: article
filename: elefunt.bib
label: Babb:1979:OEC
author: Stanley E. Babb, Jr. and James W. Cafky
title: Operational evaluation of certain infinite Bessel function integrals
journal: j-MATH-COMPUT
volume: 33
number: 147
pages: 1033--1039
month: jul
monthnumber: 7
year: 1979
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 44A99
MRnumber: 80e:44002
MRreviewer: L. Arteaga
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
classcodes: C4180 (Integral equations)
corpsource: Dept. of Phys. and Astron., Univ. of Oklahoma, Norman, OK, USA
journalURL: http://www.ams.org/mcom/
treatment: A Application; T Theoretical or Mathematical
rawauthor: Stanley E. {Babb, Jr.} and James W. Cafky
rawtitle: Operational evaluation of certain infinite {Bessel} function integrals
keywords:
Bessel function integral; integration; numerical methods; Schafheitlin method; trigonometric function; Weber

entry:
@Article{Babb:1979:OEC,
  author =       "Stanley E. {Babb, Jr.} and James W. Cafky",
  title =        "Operational evaluation of certain infinite {Bessel}
                 function integrals",
  journal =      j-MATH-COMPUT,
  volume =       "33",
  number =       "147",
  pages =        "1033--1039",
  month =        jul,
  year =         "1979",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "44A99",
  MRnumber =     "80e:44002",
  MRreviewer =   "L. Arteaga",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "C4180 (Integral equations)",
  corpsource =   "Dept. of Phys. and Astron., Univ. of Oklahoma, Norman,
                 OK, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Bessel function integral; integration; numerical
                 methods; Schafheitlin method; trigonometric function;
                 Weber",
  treatment =    "A Application; T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Borjesson:1979:SAE
author: P. Borjesson and C.-E. Sundberg
title: Simple Approximations of the Error Function $ Q(x) $ for Communications Applications
journal: j-IEEE-TRANS-COMM
volume: 27
number: 3
pages: 639--643
month: mar
monthnumber: 3
year: 1979
CODEN: IECMBT
DOI: https://doi.org/10.1109/tcom.1979.1094433
ISSN: 0090-6778 (print), 1558-0857 (electronic) OR 00906778 (print), 15580857 (electronic)
ISSNL: 0090-6778 OR 00906778
bibdate: Sat Dec 16 15:29:00 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.12.16 15:29:00 ???
fjournal: IEEE Transactions on Communications
acknowledgement: ack-nhfb
rawauthor: P. B{\"o}rjesson and C.-E. Sundberg
rawtitle: Simple Approximations of the Error Function {$ Q(x) $} for Communications Applications
entry:
@Article{Borjesson:1979:SAE,
  author =       "P. B{\"o}rjesson and C.-E. Sundberg",
  title =        "Simple Approximations of the Error Function {$ Q(x) $}
                 for Communications Applications",
  journal =      j-IEEE-TRANS-COMM,
  volume =       "27",
  number =       "3",
  pages =        "639--643",
  month =        mar,
  year =         "1979",
  CODEN =        "IECMBT",
  DOI =          "https://doi.org/10.1109/tcom.1979.1094433",
  ISSN =         "0090-6778 (print), 1558-0857 (electronic)",
  ISSN-L =       "0090-6778",
  bibdate =      "Sat Dec 16 15:29:00 2017",
  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: Campbell:1979:BFR
author: J. B. Campbell
title: Bessel functions $ J_nu (x) $ and $ Y_nu (x) $ of real order and real argument
journal: j-COMP-PHYS-COMM
volume: 18
number: 1
pages: 133--142
month: sep
monthnumber: 9
year: 1979
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/0010-4655(79)90030-4
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Mon Feb 13 06:01:26 MST 2012
bibtimestamp: 2012.02.13 06:01:26 MST
URL: http://www.sciencedirect.com/science/article/pii/0010465579900304
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: J. B. Campbell
rawtitle: {Bessel} functions {$ J_\nu (x) $} and {$ Y_\nu (x) $} of real order and real argument
entry:
@Article{Campbell:1979:BFR,
  author =       "J. B. Campbell",
  title =        "{Bessel} functions {$ J_\nu (x) $} and {$ Y_\nu (x) $}
                 of real order and real argument",
  journal =      j-COMP-PHYS-COMM,
  volume =       "18",
  number =       "1",
  pages =        "133--142",
  month =        sep,
  year =         "1979",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(79)90030-4",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Feb 13 06:01:26 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0010465579900304",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}


bibtype: article
filename: elefunt.bib
label: Carlson:1979:CEI
author: B. C. Carlson
title: Computing elliptic integrals by duplication
journal: j-NUM-MATH
volume: 33
number: 1
pages: 1--16
month: mar
monthnumber: 3
year: 1979
CODEN: NUMMA7
ISSN: 0029-599X (print), 0945-3245 (electronic) OR 0029599X (print), 09453245 (electronic)
ISSNL: 0029-599X OR 0029599X
MRclass: 65D20
MRnumber: 80h:65008
bibdate: Mon May 26 11:49:34 MDT 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.05.26 11:49:34 MDT
fjournal: Numerische Mathematik
acknowledgement: ack-nhfb
corpsource: Dept. of Math. and Phys., Iowa Univ., Ames, IA, USA
journalURL: http://link.springer.com/journal/211
treatment: A Application; T Theoretical or Mathematical
rawauthor: B. C. Carlson
rawtitle: Computing elliptic integrals by duplication
abstract:
Logarithms, arctangents, and elliptic integrals of all three kinds (including complete integrals) are evaluated numerically by successive applications of the duplication theorem. When the convergence is improved by including a fixed number of terms of Taylor's series, the error ultimately decreases by a factor of 4096 in each cycle of iteration. Except for Cauchy principal values there is no separation of cases according to the values of the variables, and no serious cancellations occur if the variables are real and nonnegative. Only rational operations and square roots are required. An appendix contains a recurrence relation and two new representations (in terms of elementary symmetric functions and power sums) for $R$-polynomials, as well as an upper bound for the error made in truncating the Taylor series of an $R$-function.

keywords:
convergence; duplication theory; elliptic integral; integration; numerical methods; R-polynomial; Taylor series

rawabstract:
Logarithms, arctangents, and elliptic integrals of all three kinds (including complete integrals) are evaluated numerically by successive applications of the duplication theorem. When the convergence is improved by including a fixed number of terms of Taylor's series, the error ultimately decreases by a factor of 4096 in each cycle of iteration. Except for Cauchy principal values there is no separation of cases according to the values of the variables, and no serious cancellations occur if the variables are real and nonnegative. Only rational operations and square roots are required. An appendix contains a recurrence relation and two new representations (in terms of elementary symmetric functions and power sums) for $R$-polynomials, as well as an upper bound for the error made in truncating the Taylor series of an $R$-function.

entry:
@Article{Carlson:1979:CEI,
  author =       "B. C. Carlson",
  title =        "Computing elliptic integrals by duplication",
  journal =      j-NUM-MATH,
  volume =       "33",
  number =       "1",
  pages =        "1--16",
  month =        mar,
  year =         "1979",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "65D20",
  MRnumber =     "80h:65008",
  bibdate =      "Mon May 26 11:49:34 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "Logarithms, arctangents, and elliptic integrals of all
                 three kinds (including complete integrals) are
                 evaluated numerically by successive applications of the
                 duplication theorem. When the convergence is improved
                 by including a fixed number of terms of Taylor's
                 series, the error ultimately decreases by a factor of
                 4096 in each cycle of iteration. Except for Cauchy
                 principal values there is no separation of cases
                 according to the values of the variables, and no
                 serious cancellations occur if the variables are real
                 and nonnegative. Only rational operations and square
                 roots are required. An appendix contains a recurrence
                 relation and two new representations (in terms of
                 elementary symmetric functions and power sums) for
                 $R$-polynomials, as well as an upper bound for the
                 error made in truncating the Taylor series of an
                 $R$-function.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classification = "C4180 (Integral equations)",
  corpsource =   "Dept. of Math. and Phys., Iowa Univ., Ames, IA, USA",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "convergence; duplication theory; elliptic integral;
                 integration; numerical methods; R-polynomial; Taylor
                 series",
  treatment =    "A Application; T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Cole:1979:EI
author: R. J. Cole and C. Pescatore
title: Evaluation of the Integral $ int _0^infty t^n exp ( - t^2 - x / t) d t $
journal: j-J-COMPUT-PHYS
volume: 32
number: 2
pages: 280--287
month: aug
monthnumber: 8
year: 1979
CODEN: JCTPAH
DOI: https://doi.org/10.1016/0021-9991(79)90135-9
ISSN: 0021-9991 (print), 1090-2716 (electronic) OR 00219991 (print), 10902716 (electronic)
ISSNL: 0021-9991 OR 00219991
bibdate: Sun Jan 1 09:15:34 MST 2012
bibtimestamp: 2012.01.01 09:15:34 MST
URL: http://www.sciencedirect.com/science/article/pii/0021999179901359
fjournal: Journal of Computational Physics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00219991/
rawauthor: R. J. Cole and C. Pescatore
rawtitle: Evaluation of the Integral $ \int_0^\infty t^n \exp ( - t^2 - x / t) \, d t $
abstract:
The main purpose of this paper is to provide a unified approach to the treatment of linear recurrence relations for single or pairs of order statistics. Suppose such a relation has been proved in the simplest case when $ X_1, ldots , X_n $ are independent variates having an arbitrary absolutely continuous distribution. It is pointed out that the same relation continues to hold when the $X$'s are exchangeable, whether continuous or not. As has recently become well known, further generalizations are possible when the $X$'s have any joint distribution. Attention is also drawn to a useful nonlinear recurrence relation due to Boncelet (1987).

rawabstract:
The main purpose of this paper is to provide a unified approach to the treatment of linear recurrence relations for single or pairs of order statistics. Suppose such a relation has been proved in the simplest case when $ X_1, \ldots {}, X_n $ are independent variates having an arbitrary absolutely continuous distribution. It is pointed out that the same relation continues to hold when the $X$'s are exchangeable, whether continuous or not. As has recently become well known, further generalizations are possible when the $X$'s have any joint distribution. Attention is also drawn to a useful nonlinear recurrence relation due to Boncelet (1987).

entry:
@Article{Cole:1979:EI,
  author =       "R. J. Cole and C. Pescatore",
  title =        "Evaluation of the Integral $ \int_0^\infty t^n \exp (
                 - t^2 - x / t) \, d t $",
  journal =      j-J-COMPUT-PHYS,
  volume =       "32",
  number =       "2",
  pages =        "280--287",
  month =        aug,
  year =         "1979",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(79)90135-9",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Sun Jan 1 09:15:34 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1970.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0021999179901359",
  abstract =     "The main purpose of this paper is to provide a unified
                 approach to the treatment of linear recurrence
                 relations for single or pairs of order statistics.
                 Suppose such a relation has been proved in the simplest
                 case when $ X_1, \ldots {}, X_n $ are independent
                 variates having an arbitrary absolutely continuous
                 distribution. It is pointed out that the same relation
                 continues to hold when the $X$'s are exchangeable,
                 whether continuous or not. As has recently become well
                 known, further generalizations are possible when the
                 $X$'s have any joint distribution. Attention is also
                 drawn to a useful nonlinear recurrence relation due to
                 Boncelet (1987).",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}


bibtype: article
filename: elefunt.bib
label: Conde:1979:Z
author: S. Conde and Shyam L. Kalla
title: The $ nu $-zeros of $ J_- nu (x) $
journal: j-MATH-COMPUT
volume: 33
number: 145
pages: 423--426
month: jan
monthnumber: 1
year: 1979
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 65D20
MRnumber: 80b:65021
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
remark: Fullerton: With a microfiche supplement.
acknowledgement: ack-nhfb
classcodes: C4170 (Differential equations); C4190 (Other numerical methods)
corpsource: Facultad de Ingenieria, Univ. del Zulia, Maracaibo, Venezuela
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: S. Conde and Shyam L. Kalla
rawtitle: The $ \nu $-zeros of {$ J_{- \nu }(x) $}
keywords:
Bessel function; boundary value; boundary-value problems; J/sub -v/(x); partial differential equations; poles and zeros; problems; transforms; v-zeros

entry:
@Article{Conde:1979:Z,
  author =       "S. Conde and Shyam L. Kalla",
  title =        "The $ \nu $-zeros of {$ J_{- \nu }(x) $}",
  journal =      j-MATH-COMPUT,
  volume =       "33",
  number =       "145",
  pages =        "423--426",
  month =        jan,
  year =         "1979",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65D20",
  MRnumber =     "80b:65021",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "C4170 (Differential equations); C4190 (Other numerical
                 methods)",
  corpsource =   "Facultad de Ingenieria, Univ. del Zulia, Maracaibo,
                 Venezuela",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Bessel function; boundary value; boundary-value
                 problems; J/sub -v/(x); partial differential equations;
                 poles and zeros; problems; transforms; v-zeros",
  remark =       "Fullerton: With a microfiche supplement.",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Delic:1979:CSS
author: G. Delic
title: Chebyshev series for the spherical Bessel function $ j_l(r) $
journal: j-COMP-PHYS-COMM
volume: 18
number: 1
pages: 73--86
month: sep
monthnumber: 9
year: 1979
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/0010-4655(79)90025-0
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Mon Feb 13 06:01:26 MST 2012
bibtimestamp: 2012.02.13 06:01:26 MST
URL: http://www.sciencedirect.com/science/article/pii/0010465579900250
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: G. Delic
rawtitle: {Chebyshev} series for the spherical {Bessel} function $ j_l(r) $
entry:
@Article{Delic:1979:CSS,
  author =       "G. Delic",
  title =        "{Chebyshev} series for the spherical {Bessel} function
                 $ j_l(r) $",
  journal =      j-COMP-PHYS-COMM,
  volume =       "18",
  number =       "1",
  pages =        "73--86",
  month =        sep,
  year =         "1979",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(79)90025-0",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Feb 13 06:01:26 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0010465579900250",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}


bibtype: article
filename: elefunt.bib
label: Divgi:1979:CUB
author: D. R. Divgi
title: Calculation of Univariate and Bivariate Normal Probability Functions
journal: j-ANN-STAT
volume: 7
number: 4
pages: 903--910
month: jul
monthnumber: 7
year: 1979
CODEN: ASTSC7
DOI: https://doi.org/10.1214/aos/1176344739
ISSN: 0090-5364 (print), 2168-8966 (electronic) OR 00905364 (print), 21688966 (electronic)
ISSNL: 0090-5364 OR 00905364
bibdate: Wed Jun 4 06:39:50 MDT 2014
bibtimestamp: 2014.06.04 06:39:50 MDT
URL: http://projecteuclid.org/euclid.aos/1176344739
fjournal: Annals of Statistics
acknowledgement: ack-nhfb
journalURL: http://projecteuclid.org/all/euclid.aos/
rawauthor: D. R. Divgi
rawtitle: Calculation of Univariate and Bivariate Normal Probability Functions
bibsource:
https://www.math.utah.edu/pub/tex/bib/annstat1970.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Divgi:1979:CUB,
  author =       "D. R. Divgi",
  title =        "Calculation of Univariate and Bivariate Normal
                 Probability Functions",
  journal =      j-ANN-STAT,
  volume =       "7",
  number =       "4",
  pages =        "903--910",
  month =        jul,
  year =         "1979",
  CODEN =        "ASTSC7",
  DOI =          "https://doi.org/10.1214/aos/1176344739",
  ISSN =         "0090-5364 (print), 2168-8966 (electronic)",
  ISSN-L =       "0090-5364",
  bibdate =      "Wed Jun 4 06:39:50 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/annstat1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://projecteuclid.org/euclid.aos/1176344739",
  acknowledgement = ack-nhfb,
  fjournal =     "Annals of Statistics",
  journal-URL =  "http://projecteuclid.org/all/euclid.aos/",
}


bibtype: article
filename: elefunt.bib
label: Einarsson:1979:BEN
author: Bo Einarsson
title: Bibliography on the evaluation of numerical software
journal: j-J-COMPUT-APPL-MATH
volume: 5
number: 2
pages: 145--159
month: jun
monthnumber: 6
year: 1979
CODEN: JCAMDI
DOI: https://doi.org/10.1016/0771-050X(79)90011-1
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Thu Oct 28 17:14:49 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.28 17:14:49 ???
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Bo Einarsson
rawtitle: Bibliography on the evaluation of numerical software
abstract:
This bibliography on the evaluation of numerical software has been written at the request of the IFIP Working Group on Numerical Software (IFIP WG 2.5), and is divided into nine different sections. Within each section the references are given in alphabetical order by the first author. The aim of the bibliography is to be useful in the production and evaluation of good software for numerical mathematics.

TOC:
2. Miscellaneous evaluations 3. Linear algebra 4. Optimization and nonlinear equations 5. Functions 6. Quadrature 7. Integral equations 8. Ordinary differential equations 9. Partial differential equations

rawabstract:
This bibliography on the evaluation of numerical software has been written at the request of the IFIP Working Group on Numerical Software (IFIP WG 2.5), and is divided into nine different sections. Within each section the references are given in alphabetical order by the first author. The aim of the bibliography is to be useful in the production and evaluation of good software for numerical mathematics.

rawTOC:
2. Miscellaneous evaluations \\ 3. Linear algebra \\ 4. Optimization and nonlinear equations \\ 5. Functions \\ 6. Quadrature \\ 7. Integral equations \\ 8. Ordinary differential equations \\ 9. Partial differential equations

entry:
@Article{Einarsson:1979:BEN,
  author =       "Bo Einarsson",
  title =        "Bibliography on the evaluation of numerical software",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "5",
  number =       "2",
  pages =        "145--159",
  month =        jun,
  year =         "1979",
  CODEN =        "JCAMDI",
  DOI =          "https://doi.org/10.1016/0771-050X(79)90011-1",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Thu Oct 28 17:14:49 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "This bibliography on the evaluation of numerical
                 software has been written at the request of the IFIP
                 Working Group on Numerical Software (IFIP WG 2.5), and
                 is divided into nine different sections. Within each
                 section the references are given in alphabetical order
                 by the first author. The aim of the bibliography is to
                 be useful in the production and evaluation of good
                 software for numerical mathematics.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
  tableofcontents = "2. Miscellaneous evaluations \\
                 3. Linear algebra \\
                 4. Optimization and nonlinear equations \\
                 5. Functions \\
                 6. Quadrature \\
                 7. Integral equations \\
                 8. Ordinary differential equations \\
                 9. Partial differential equations",
}


bibtype: article
filename: elefunt.bib
label: elLozy:1979:RAS
author: Mohamed el Lozy
journal: j-TOMS
volume: 5
number: 2
pages: 238--239
month: jun
monthnumber: 6
year: 1979
CODEN: ACMSCU
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Tue Feb 06 05:28:16 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1996.02.06 05:28:16 ???
note: See cite Hill:1970:AASa,Hill:1970:AASb,Hill:1981:RSD,Hill:1985:RCS.
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Mohamed el Lozy
rawnote: See \cite{Hill:1970:AASa,Hill:1970:AASb,Hill:1981:RSD,Hill:1985:RCS}.
title:
Remark on ``Algorithm 395: Student's $t$-Distribution'' and Remark on ``Algorithm 396: Student's Quantiles [S14]''

remark:
Fullerton: The algorithms are corrected for computers with anomalously small word lengths (e.g., IBM and Interdata).

rawtitle:
Remark on ``{Algorithm 395: Student's $t$-Distribution}'' and Remark on ``{Algorithm 396: Student's Quantiles [S14]}''

entry:
@Article{elLozy:1979:RAS,
  author =       "Mohamed el Lozy",
  title =        "Remark on ``{Algorithm 395: Student's
                 $t$-Distribution}'' and Remark on ``{Algorithm 396:
                 Student's Quantiles [S14]}''",
  journal =      j-TOMS,
  volume =       "5",
  number =       "2",
  pages =        "238--239",
  month =        jun,
  year =         "1979",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Feb 06 05:28:16 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See
                 \cite{Hill:1970:AASa,Hill:1970:AASb,Hill:1981:RSD,Hill:1985:RCS}.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  remark =       "Fullerton: The algorithms are corrected for computers
                 with anomalously small word lengths (e.g., IBM and
                 Interdata).",
}


bibtype: article
filename: elefunt.bib
label: Epstein:1979:STE
author: H. I. Epstein and B. F. Caviness
title: A structure theorem for the elementary functions and its application to the identity problem
journal: j-INT-J-COMPUT-INF-SCI
volume: 8
number: 1
pages: 9--37
year: 1979
CODEN: IJCIAH
ISSN: 0091-7036 OR 00917036
MRclass: 12H05 (68C05)
MRnumber: 80k:12032
MRreviewer: Michael F. Singer
bibdate: Sat Apr 26 12:45:53 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.04.26 12:45:53 ???
fjournal: International Journal of Computer and Information Sciences
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10766
rawauthor: H. I. Epstein and B. F. Caviness
rawtitle: A structure theorem for the elementary functions and its application to the identity problem
entry:
@Article{Epstein:1979:STE,
  author =       "H. I. Epstein and B. F. Caviness",
  title =        "A structure theorem for the elementary functions and
                 its application to the identity problem",
  journal =      j-INT-J-COMPUT-INF-SCI,
  volume =       "8",
  number =       "1",
  pages =        "9--37",
  year =         "1979",
  CODEN =        "IJCIAH",
  ISSN =         "0091-7036",
  MRclass =      "12H05 (68C05)",
  MRnumber =     "80k:12032",
  MRreviewer =   "Michael F. Singer",
  bibdate =      "Sat Apr 26 12:45:53 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Computer and Information
                 Sciences",
  journal-URL =  "http://link.springer.com/journal/10766",
}


bibtype: article
filename: elefunt.bib
label: Fettis:1979:AEU
author: Henry E. Fettis
title: An asymptotic expansion for the upper percentage points of the $ chi ^2 $-distribution
journal: j-MATH-COMPUT
volume: 33
number: 147
pages: 1059--1064
month: jul
monthnumber: 7
year: 1979
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 62E20
MRnumber: 80h:62014
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
keywords: approximation theory; asymptotic expansion; upper percentage point
acknowledgement: ack-nhfb
classcodes: C4130 (Interpolation and function approximation)
journalURL: http://www.ams.org/mcom/
treatment: A Application; T Theoretical or Mathematical
rawauthor: Henry E. Fettis
rawtitle: An asymptotic expansion for the upper percentage points of the $ \chi^2 $-distribution
entry:
@Article{Fettis:1979:AEU,
  author =       "Henry E. Fettis",
  title =        "An asymptotic expansion for the upper percentage
                 points of the $ \chi^2 $-distribution",
  journal =      j-MATH-COMPUT,
  volume =       "33",
  number =       "147",
  pages =        "1059--1064",
  month =        jul,
  year =         "1979",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "62E20",
  MRnumber =     "80h:62014",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "C4130 (Interpolation and function approximation)",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "approximation theory; asymptotic expansion; upper
                 percentage point",
  treatment =    "A Application; T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Gabutti:1979:HPM
author: Bruno Gabutti
title: On high precision methods for computing integrals involving Bessel functions
journal: j-MATH-COMPUT
volume: 33
number: 147
pages: 1049--1057
month: jul
monthnumber: 7
year: 1979
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 65D30
MRnumber: 80c:65048
MRreviewer: K. Jetter
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
keywords: Bessel function integral; computational complexity; exponential function integral; integration
acknowledgement: ack-nhfb
classcodes: C4180 (Integral equations); C4240 (Programming and algorithm theory)
corpsource: Istituto di Calcoli Numerici, Univ. di Torino, Torino, Italy
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: Bruno Gabutti
rawtitle: On high precision methods for computing integrals involving {Bessel} functions
entry:
@Article{Gabutti:1979:HPM,
  author =       "Bruno Gabutti",
  title =        "On high precision methods for computing integrals
                 involving {Bessel} functions",
  journal =      j-MATH-COMPUT,
  volume =       "33",
  number =       "147",
  pages =        "1049--1057",
  month =        jul,
  year =         "1979",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65D30",
  MRnumber =     "80c:65048",
  MRreviewer =   "K. Jetter",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "C4180 (Integral equations); C4240 (Programming and
                 algorithm theory)",
  corpsource =   "Istituto di Calcoli Numerici, Univ. di Torino, Torino,
                 Italy",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Bessel function integral; computational complexity;
                 exponential function integral; integration",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Gargantini:1979:NSS
author: Irene Gargantini
title: The Numerical Stability of Simultaneous Iterations Via Square-Rooting
journal: j-COMPUT-MATH-APPL
volume: 5
number: 1
pages: 25--31
year: 1979
CODEN: CMAPDK
DOI: https://doi.org/10.1016/0898-1221(81)90136-X
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Wed Mar 1 18:51:16 MST 2017
bibtimestamp: 2017.03.01 18:51:16 MST
URL: http://www.sciencedirect.com/science/article/pii/089812218190136X
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-jr
journalURL: http://www.sciencedirect.com/science/journal/08981221
rawauthor: Irene Gargantini
rawtitle: The Numerical Stability of Simultaneous Iterations Via Square-Rooting
bibsource:
https://www.math.utah.edu/pub/tex/bib/computmathappl1970.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Gargantini:1979:NSS,
  author =       "Irene Gargantini",
  title =        "The Numerical Stability of Simultaneous Iterations Via
                 Square-Rooting",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "5",
  number =       "1",
  pages =        "25--31",
  month =        "????",
  year =         "1979",
  CODEN =        "CMAPDK",
  DOI =          "https://doi.org/10.1016/0898-1221(81)90136-X",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 18:51:16 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/089812218190136X",
  acknowledgement = ack-jr # " and " # ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}


bibtype: article
filename: elefunt.bib
label: Gautschi:1979:AIG
author: W. Gautschi
title: Algorithm 542: Incomplete Gamma Functions [S14]
journal: j-TOMS
volume: 5
number: 4
pages: 482--489
month: dec
monthnumber: 12
year: 1979
CODEN: ACMSCU
DOI: https://doi.org/10.1145/355853.355864
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Sun Aug 28 00:39:50 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.08.28 00:39:50 ???
fjournal: ACM Transactions on Mathematical Software (TOMS)
remark: Fullerton: FORTRAN routines of adjustable accuracy.
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: W. Gautschi
rawtitle: {Algorithm 542}: Incomplete Gamma Functions [{S14}]
entry:
@Article{Gautschi:1979:AIG,
  author =       "W. Gautschi",
  title =        "{Algorithm 542}: Incomplete Gamma Functions [{S14}]",
  journal =      j-TOMS,
  volume =       "5",
  number =       "4",
  pages =        "482--489",
  month =        dec,
  year =         "1979",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355853.355864",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Aug 28 00:39:50 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  remark =       "Fullerton: FORTRAN routines of adjustable accuracy.",
}


bibtype: article
filename: elefunt.bib
label: Gautschi:1979:CPI
author: Walter Gautschi
title: A Computational Procedure for Incomplete Gamma Functions
journal: j-TOMS
volume: 5
number: 4
pages: 466--481
month: dec
monthnumber: 12
year: 1979
CODEN: ACMSCU
DOI: https://doi.org/10.1145/355853.355863
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Sun Aug 28 00:32:50 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.08.28 00:32:50 ???
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Walter Gautschi
rawtitle: A Computational Procedure for Incomplete Gamma Functions
remark:
Fullerton: Algorithms for the incomplete gamma function, $ gamma (a, x) $, the complementary function, $ Gamma (a, x) $, and Tricomi's form, $ gamma '(a, x) $, are given.

entry:
@Article{Gautschi:1979:CPI,
  author =       "Walter Gautschi",
  title =        "A Computational Procedure for Incomplete Gamma
                 Functions",
  journal =      j-TOMS,
  volume =       "5",
  number =       "4",
  pages =        "466--481",
  month =        dec,
  year =         "1979",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355853.355863",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Aug 28 00:32:50 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  remark =       "Fullerton: Algorithms for the incomplete gamma
                 function, $ \gamma (a, x) $, the complementary
                 function, $ \Gamma (a, x) $, and Tricomi's form, $
                 \gamma '(a, x) $, are given.",
}


bibtype: article
filename: elefunt.bib
label: Glasser:1979:NI
author: M. L. Glasser
journal: j-MATH-COMPUT
volume: 33
number: 146
pages: 792--793
month: apr
monthnumber: 4
year: 1979
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 33A40
MRnumber: 80d:33004
MRreviewer: T. Erber
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
keywords: Bessel functions; hypergeometric series; integral; integral equations
acknowledgement: ack-nhfb
classcodes: C1120 (Mathematical analysis); C4180 (Integral equations)
corpsource: Math. and Computer Sci. Dept., Clarkson Coll. of Technol., Potsdam, NY, USA
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: M. L. Glasser
title:
A Note on the Integral $ int ^infty _0 t^2 alpha - 1(1 + t^2)^1 - alpha - beta J_nu (x sqrt 1 + t^2) d t $

rawtitle:
A Note on the Integral $ \int^\infty_0 t^{2 \alpha - 1}(1 + t^2)^{1 - \alpha - \beta } {J}_\nu (x \sqrt {1 + t^2}) d t $

entry:
@Article{Glasser:1979:NI,
  author =       "M. L. Glasser",
  title =        "A Note on the Integral $ \int^\infty_0 t^{2 \alpha -
                 1}(1 + t^2)^{1 - \alpha - \beta } {J}_\nu (x \sqrt {1 +
                 t^2}) d t $",
  journal =      j-MATH-COMPUT,
  volume =       "33",
  number =       "146",
  pages =        "792--793",
  month =        apr,
  year =         "1979",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "33A40",
  MRnumber =     "80d:33004",
  MRreviewer =   "T. Erber",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "C1120 (Mathematical analysis); C4180 (Integral
                 equations)",
  corpsource =   "Math. and Computer Sci. Dept., Clarkson Coll. of
                 Technol., Potsdam, NY, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Bessel functions; hypergeometric series; integral;
                 integral equations",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Haavie:1979:GNT
author: Tore Haa vie
title: Generalized Neville type extrapolation schemes
journal: j-BIT
volume: 19
number: 2
pages: 204--213
month: jun
monthnumber: 6
year: 1979
CODEN: BITTEL, NBITAB
DOI: https://doi.org/10.1007/BF01930850
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
ISSNL: 0006-3835 OR 00063835
MRclass: 65B05 (65D05 65D30)
MRnumber: 80f:65005
MRreviewer: Siegfried Filippi
bibdate: Wed Jan 4 18:52:16 MST 2006
bibtimestamp: 2006.01.04 18:52:16 MST
URL: http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=19&issue=2&spage=204
fjournal: BIT (Nordisk tidskrift for informationsbehandling)
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10543
rawauthor: Tore H{\aa}vie
rawtitle: Generalized {Neville} type extrapolation schemes
bibsource:
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=19&issue=2; https://www.math.utah.edu/pub/tex/bib/bit.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Haavie:1979:GNT,
  author =       "Tore H{\aa}vie",
  title =        "Generalized {Neville} type extrapolation schemes",
  journal =      j-BIT,
  volume =       "19",
  number =       "2",
  pages =        "204--213",
  month =        jun,
  year =         "1979",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01930850",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "65B05 (65D05 65D30)",
  MRnumber =     "80f:65005",
  MRreviewer =   "Siegfried Filippi",
  bibdate =      "Wed Jan 4 18:52:16 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=19&issue=2;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=19&issue=2&spage=204",
  acknowledgement = ack-nhfb,
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}


bibtype: article
filename: elefunt.bib
label: Johnson:1979:RAF
author: Donald B. Johnson and Webb Miller and Brian Minnihan and Celia Wrathall
title: Reducibility Among Floating-Point Graphs
journal: j-J-ACM
volume: 26
number: 4
pages: 739--760
month: oct
monthnumber: 10
year: 1979
CODEN: JACOAH
ISSN: 0004-5411 (print), 1557-735X (electronic) OR 00045411 (print), 1557735X (electronic)
ISSNL: 0004-5411 OR 00045411
MRclass: 65G05
MRnumber: 80i:65045
bibdate: Fri Dec 08 11:55:10 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1995.12.08 11:55:10 ???
fjournal: Journal of the ACM
acknowledgement: ack-nhfb
ajournal: J. Assoc. Comput. Mach.
journalURL: https://dl.acm.org/loi/jacm
rawauthor: Donald B. Johnson and Webb Miller and Brian Minnihan and Celia Wrathall
rawtitle: Reducibility Among Floating-Point Graphs
abstract:
The graph-theoretic models of this paper can be used to compare the rounding-error behavior of numerical programs. The models follow the approach, popularized by Wilkinson, of assuming independent rounding errors in each arithmetic operation. Models constructed on this assumption are more tractable than would be the case under more realistic assumptions. There are identified two easily tested conditions on programs which guarantee that error analyses are relatively insensitive to the particular graph model employed. The development has the additional benefit of sometimes providing an elementary proof that one program is comparable in stability to another. Examples of such results are given.

rawabstract:
The graph-theoretic models of this paper can be used to compare the rounding-error behavior of numerical programs. The models follow the approach, popularized by Wilkinson, of assuming independent rounding errors in each arithmetic operation. Models constructed on this assumption are more tractable than would be the case under more realistic assumptions. There are identified two easily tested conditions on programs which guarantee that error analyses are relatively insensitive to the particular graph model employed. The development has the additional benefit of sometimes providing an elementary proof that one program is comparable in stability to another. Examples of such results are given.

entry:
@Article{Johnson:1979:RAF,
  author =       "Donald B. Johnson and Webb Miller and Brian Minnihan
                 and Celia Wrathall",
  title =        "Reducibility Among Floating-Point Graphs",
  journal =      j-J-ACM,
  volume =       "26",
  number =       "4",
  pages =        "739--760",
  month =        oct,
  year =         "1979",
  CODEN =        "JACOAH",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  MRclass =      "65G05",
  MRnumber =     "80i:65045",
  bibdate =      "Fri Dec 08 11:55:10 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "The graph-theoretic models of this paper can be used
                 to compare the rounding-error behavior of numerical
                 programs. The models follow the approach, popularized
                 by Wilkinson, of assuming independent rounding errors
                 in each arithmetic operation. Models constructed on
                 this assumption are more tractable than would be the
                 case under more realistic assumptions. There are
                 identified two easily tested conditions on programs
                 which guarantee that error analyses are relatively
                 insensitive to the particular graph model employed. The
                 development has the additional benefit of sometimes
                 providing an elementary proof that one program is
                 comparable in stability to another. Examples of such
                 results are given.",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Assoc. Comput. Mach.",
  fjournal =     "Journal of the ACM",
  journal-URL =  "https://dl.acm.org/loi/jacm",
}


bibtype: article
filename: elefunt.bib
label: Kusterer:1979:SEP
author: Roland Kusterer and Manfred Reimer
title: Stable Evaluation of Polynomials in Time $ log n $
journal: j-MATH-COMPUT
volume: 33
number: 147
pages: 1019--1031
month: jul
monthnumber: 7
year: 1979
CODEN: MCMPAF
DOI: https://doi.org/10.1090/S0025-5718-1979-0528054-X; https://doi.org/10.2307/2006075
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 65G05 (68C25)
MRnumber: 80d:65050 (528054)
MRreviewer: C. W. Clenshaw
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
keywords: algorithm; approximation theory; number of multiplications to evaluate a polynomial; polynomials
acknowledgement: ack-nhfb
classcodes: C4130 (Interpolation and function approximation)
corpsource: Math. Inst., University of Dortmund, Dortmund, West Germany
journalURL: http://www.ams.org/mcom/
treatment: A Application; T Theoretical or Mathematical
rawauthor: Roland Kusterer and Manfred Reimer
rawtitle: Stable Evaluation of Polynomials in Time $ \log n $
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt; https://www.math.utah.edu/pub/bibnet/authors/c/clenshaw-charles-w.bib; https://www.math.utah.edu/pub/bibnet/authors/t/todd-john.bib; 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/mathcomp1970.bib; JSTOR database

entry:
@Article{Kusterer:1979:SEP,
  author =       "Roland Kusterer and Manfred Reimer",
  title =        "Stable Evaluation of Polynomials in Time $ \log n $",
  journal =      j-MATH-COMPUT,
  volume =       "33",
  number =       "147",
  pages =        "1019--1031",
  month =        jul,
  year =         "1979",
  CODEN =        "MCMPAF",
  DOI =          "https://doi.org/10.1090/S0025-5718-1979-0528054-X;
                 https://doi.org/10.2307/2006075",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65G05 (68C25)",
  MRnumber =     "80d:65050 (528054)",
  MRreviewer =   "C. W. Clenshaw",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/bibnet/authors/c/clenshaw-charles-w.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/t/todd-john.bib;
                 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/mathcomp1970.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "C4130 (Interpolation and function approximation)",
  corpsource =   "Math. Inst., University of Dortmund, Dortmund, West
                 Germany",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "algorithm; approximation theory; number of
                 multiplications to evaluate a polynomial; polynomials",
  reviewer-dates = "Charles William Clenshaw (15 March 1926--23
                 September 2004)",
  treatment =    "A Application; T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Leung:1979:AFE
author: K. V. Leung and S. S. Ghaderpanah
journal: j-MATH-COMPUT
volume: 33
number: 148
pages: 1299--1306
month: oct
monthnumber: 10
year: 1979
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 65D20 (33-04)
MRnumber: 80e:65024
MRreviewer: R. P. Boas, Jr.
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
classcodes: C4140 (Linear algebra)
corpsource: Dept. of Computer Sci., Concordia Univ., Montreal, Que., Canada
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: K. V. Leung and S. S. Ghaderpanah
title:
An application of the finite element approximation method to find the complex zeros of the modified Bessel function $ K_n(z) $

keywords:
Bessel function; complex zeros; finite element analysis; finite element approximation method; iterative optimisation scheme; modified; poles and zeros

rawtitle:
An application of the finite element approximation method to find the complex zeros of the modified {Bessel} function $ {K}_n(z) $

entry:
@Article{Leung:1979:AFE,
  author =       "K. V. Leung and S. S. Ghaderpanah",
  title =        "An application of the finite element approximation
                 method to find the complex zeros of the modified
                 {Bessel} function $ {K}_n(z) $",
  journal =      j-MATH-COMPUT,
  volume =       "33",
  number =       "148",
  pages =        "1299--1306",
  month =        oct,
  year =         "1979",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65D20 (33-04)",
  MRnumber =     "80e:65024",
  MRreviewer =   "R. P. Boas, Jr.",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "C4140 (Linear algebra)",
  corpsource =   "Dept. of Computer Sci., Concordia Univ., Montreal,
                 Que., Canada",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Bessel function; complex zeros; finite element
                 analysis; finite element approximation method;
                 iterative optimisation scheme; modified; poles and
                 zeros",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Lindstrom:1979:MSM
author: F. T. Lindstrom
title: A Modified $3$-Spline Method for Evaluating the Euler Digamma Function
journal: j-TECHNOMETRICS
volume: 21
number: 3
pages: 307--311
month: aug
monthnumber: 8
year: 1979
CODEN: TCMTA2
DOI: https://doi.org/10.2307/1267752
ISSN: 0040-1706 (print), 1537-2723 (electronic) OR 00401706 (print), 15372723 (electronic)
ISSNL: 0040-1706 OR 00401706
bibdate: Sat Jun 21 13:18:50 MDT 2014
bibtimestamp: 2014.06.21 13:18:50 MDT
URL: http://www.jstor.org/stable/1267752
fjournal: Technometrics
acknowledgement: ack-nhfb
journalURL: http://www.jstor.org/journals/00401706.html
rawauthor: F. T. Lindstrom
rawtitle: A Modified $3$-Spline Method for Evaluating the {Euler} Digamma Function
bibsource:
http://www.jstor.org/journals/00401706.html; http://www.jstor.org/stable/i254300; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/technometrics1970.bib

entry:
@Article{Lindstrom:1979:MSM,
  author =       "F. T. Lindstrom",
  title =        "A Modified $3$-Spline Method for Evaluating the
                 {Euler} Digamma Function",
  journal =      j-TECHNOMETRICS,
  volume =       "21",
  number =       "3",
  pages =        "307--311",
  month =        aug,
  year =         "1979",
  CODEN =        "TCMTA2",
  DOI =          "https://doi.org/10.2307/1267752",
  ISSN =         "0040-1706 (print), 1537-2723 (electronic)",
  ISSN-L =       "0040-1706",
  bibdate =      "Sat Jun 21 13:18:50 MDT 2014",
  bibsource =    "http://www.jstor.org/journals/00401706.html;
                 http://www.jstor.org/stable/i254300;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/technometrics1970.bib",
  URL =          "http://www.jstor.org/stable/1267752",
  acknowledgement = ack-nhfb,
  fjournal =     "Technometrics",
  journal-URL =  "http://www.jstor.org/journals/00401706.html",
}


bibtype: article
filename: elefunt.bib
label: Ling:1979:EWZ
author: C. B. Ling
title: Evaluation of Weierstrass Zeta Functions
journal: j-SIAM-REVIEW
volume: 21
number: 1
pages: 146--147
year: 1979
CODEN: SIREAD
DOI: https://doi.org/10.1137/1021020
ISSN: 0036-1445 (print), 1095-7200 (electronic) OR 00361445 (print), 10957200 (electronic)
ISSNL: 0036-1445 OR 00361445
bibdate: Fri Jun 21 11:25:02 MDT 2013
bibtimestamp: 2013.06.21 11:25:02 MDT
fjournal: SIAM Review
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sirev
rawauthor: C. B. Ling
rawtitle: Evaluation of {Weierstrass} Zeta Functions
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib

entry:
@Article{Ling:1979:EWZ,
  author =       "C. B. Ling",
  title =        "Evaluation of {Weierstrass} Zeta Functions",
  journal =      j-SIAM-REVIEW,
  volume =       "21",
  number =       "1",
  pages =        "146--147",
  month =        "????",
  year =         "1979",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/1021020",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Fri Jun 21 11:25:02 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
}


bibtype: article
filename: elefunt.bib
label: Maurone:1979:ABD
author: Philip A. Maurone and Alain J. Phares
title: On the asymptotic behavior of the derivatives of Airy functions
journal: j-J-MATH-PHYS
volume: 20
number: 11
pages: 2191--2191
month: nov
monthnumber: 11
year: 1979
CODEN: JMAPAQ
DOI: https://doi.org/10.1063/1.523997
ISSNL: 0022-2488 OR 00222488
MRclass: 33A60
MRnumber: 80j:33014
bibdate: Sat Oct 29 11:28:40 MDT 2011
bibtimestamp: 2011.10.29 11:28:40 MDT
URL: http://jmp.aip.org/resource/1/jmapaq/v20/i11/p2191_s1
fjournal: Journal of Mathematical Physics
acknowledgement: ack-nhfb
corpsource: Dept. of Phys., Villanova Univ., Villanova, PA, USA
journalURL: http://jmp.aip.org/
onlinedate: 29 July 2008
treatment: T Theoretical or Mathematical
rawauthor: Philip A. Maurone and Alain J. Phares
rawtitle: On the asymptotic behavior of the derivatives of {Airy} functions
bibsource:
http://jmp.aip.org/; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jmathphys1975.bib

keywords:
Airy functions; angular momentum theory; asymptotic behavior; derivatives; functional analysis; noniterative functional solution; quantum theory; quark confinement; recursion relation

entry:
@Article{Maurone:1979:ABD,
  author =       "Philip A. Maurone and Alain J. Phares",
  title =        "On the asymptotic behavior of the derivatives of
                 {Airy} functions",
  journal =      j-J-MATH-PHYS,
  volume =       "20",
  number =       "11",
  pages =        "2191--2191",
  month =        nov,
  year =         "1979",
  CODEN =        "JMAPAQ",
  DOI =          "https://doi.org/10.1063/1.523997",
  ISSN =         "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
  ISSN-L =       "0022-2488",
  MRclass =      "33A60",
  MRnumber =     "80j:33014",
  bibdate =      "Sat Oct 29 11:28:40 MDT 2011",
  bibsource =    "http://jmp.aip.org/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jmathphys1975.bib",
  URL =          "http://jmp.aip.org/resource/1/jmapaq/v20/i11/p2191_s1",
  acknowledgement = ack-nhfb,
  classification = "A0230 (Function theory, analysis); A0365D
                 (Functional analytical methods in quantum theory);
                 A1235 (Composite models of particles)",
  corpsource =   "Dept. of Phys., Villanova Univ., Villanova, PA, USA",
  fjournal =     "Journal of Mathematical Physics",
  journal-URL =  "http://jmp.aip.org/",
  keywords =     "Airy functions; angular momentum theory; asymptotic
                 behavior; derivatives; functional analysis;
                 noniterative functional solution; quantum theory; quark
                 confinement; recursion relation",
  onlinedate =   "29 July 2008",
  pagecount =    "1",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Morris:1979:DFR
author: Robert Morris
title: The Dilogarithm Function of a Real Argument
journal: j-MATH-COMPUT
volume: 33
number: 146
pages: 778--787
month: apr
monthnumber: 4
year: 1979
CODEN: MCMPAF
DOI: https://doi.org/10.1090/S0025-5718-1979-0521291-X
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 65D20 (33A70)
MRnumber: 80e:65025
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
keywords: algorithm theory; dilogarithm function; real argument
acknowledgement: ack-nhfb
classcodes: C4240 (Programming and algorithm theory)
corpsource: Bell Labs., Murray Hill, NJ, USA
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: Robert Morris
rawtitle: The Dilogarithm Function of a Real Argument
remark:
Fullerton: Relative errors down to $ 10^-24 $ for $ operatorname Li_2 (z) = - int _0^z frac log (1 - z)z d z $. $ operatorname Li_2 (z) $ is a form of Spence's integral.

entry:
@Article{Morris:1979:DFR,
  author =       "Robert Morris",
  title =        "The Dilogarithm Function of a Real Argument",
  journal =      j-MATH-COMPUT,
  volume =       "33",
  number =       "146",
  pages =        "778--787",
  month =        apr,
  year =         "1979",
  CODEN =        "MCMPAF",
  DOI =          "https://doi.org/10.1090/S0025-5718-1979-0521291-X",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65D20 (33A70)",
  MRnumber =     "80e:65025",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "C4240 (Programming and algorithm theory)",
  corpsource =   "Bell Labs., Murray Hill, NJ, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "algorithm theory; dilogarithm function; real
                 argument",
  received =     "22 May 1978",
  remark =       "Fullerton: Relative errors down to $ 10^{-24} $ for $
                 \operatorname {Li}_2 (z) = - \int_0^z \frac {\log (1 -
                 z)z} \, d z $. $ \operatorname {Li}_2 (z) $ is a form
                 of Spence's integral.",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Pexton:1979:DRT
author: Robert L. Pexton and Arno D. Steiger
title: Degenerate roots of three transcendental equations involving spherical Bessel functions
journal: j-MATH-COMPUT
volume: 33
number: 147
pages: 1041--1048
month: jul
monthnumber: 7
year: 1979
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: loose microfiche suppl. 65H10 (65D20)
MRnumber: 80g:65057
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
keywords: function approximation; spherical Bessel function; transcendental equation
acknowledgement: ack-nhfb
classcodes: C4130 (Interpolation and function approximation)
corpsource: Lawrence Livermore Lab., Univ. of California, Livermore, CA, USA
journalURL: http://www.ams.org/mcom/
treatment: A Application; T Theoretical or Mathematical
rawauthor: Robert L. Pexton and Arno D. Steiger
rawtitle: Degenerate roots of three transcendental equations involving spherical {Bessel} functions
entry:
@Article{Pexton:1979:DRT,
  author =       "Robert L. Pexton and Arno D. Steiger",
  title =        "Degenerate roots of three transcendental equations
                 involving spherical {Bessel} functions",
  journal =      j-MATH-COMPUT,
  volume =       "33",
  number =       "147",
  pages =        "1041--1048",
  month =        jul,
  year =         "1979",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "loose microfiche suppl. 65H10 (65D20)",
  MRnumber =     "80g:65057",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "C4130 (Interpolation and function approximation)",
  corpsource =   "Lawrence Livermore Lab., Univ. of California,
                 Livermore, CA, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "function approximation; spherical Bessel function;
                 transcendental equation",
  treatment =    "A Application; T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Phillips:1979:FAC
author: G. Phillips
title: A fast approximation to the complementary error function for use in fitting gamma-ray peaks
journal: j-NUCL-INSTR-METH
volume: 164
pages: 561--563
month: sep
monthnumber: 9
year: 1979
CODEN: NUIMAL
DOI: https://doi.org/10.1016/0029-554X(79)90094-6
ISSN: 0029-554x (print), 1878-3759 (electronic) OR 0029554x (print), 18783759 (electronic)
ISSNL: 0029-554X OR 0029554X
bibdate: Mon Oct 24 11:37:20 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2011.10.24 11:37:20 ???
URL: http://adsabs.harvard.edu/abs/1979NucIM.164..561P
fjournal: Nuclear Instruments and Methods
acknowledgement: ack-nhfb
rawauthor: G. Phillips
rawtitle: A fast approximation to the complementary error function for use in fitting gamma-ray peaks
abstract:
A fast approximation to the complementary error function has been programmed and tested for use in the peak-shape function for fitting peaks in gamma-ray spectra. The function was compared for speed and accuracy on the NRL ASC 7 computer to the mathematical library version of the complementary error function. The approximation has resulted in a 50% time savings in the computer program HYPERMET which was developed at NRL for automatic analysis of gamma-ray spectra from germanium detectors.

rawabstract:
A fast approximation to the complementary error function has been programmed and tested for use in the peak-shape function for fitting peaks in gamma-ray spectra. The function was compared for speed and accuracy on the NRL ASC 7 computer to the mathematical library version of the complementary error function. The approximation has resulted in a 50\% time savings in the computer program HYPERMET which was developed at NRL for automatic analysis of gamma-ray spectra from germanium detectors.

entry:
@Article{Phillips:1979:FAC,
  author =       "G. Phillips",
  title =        "A fast approximation to the complementary error
                 function for use in fitting gamma-ray peaks",
  journal =      j-NUCL-INSTR-METH,
  volume =       "164",
  number =       "??",
  pages =        "561--563",
  month =        sep,
  year =         "1979",
  CODEN =        "NUIMAL",
  DOI =          "https://doi.org/10.1016/0029-554X(79)90094-6",
  ISSN =         "0029-554x (print), 1878-3759 (electronic)",
  ISSN-L =       "0029-554X",
  bibdate =      "Mon Oct 24 11:37:20 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://adsabs.harvard.edu/abs/1979NucIM.164..561P",
  abstract =     "A fast approximation to the complementary error
                 function has been programmed and tested for use in the
                 peak-shape function for fitting peaks in gamma-ray
                 spectra. The function was compared for speed and
                 accuracy on the NRL ASC 7 computer to the mathematical
                 library version of the complementary error function.
                 The approximation has resulted in a 50\% time savings
                 in the computer program HYPERMET which was developed at
                 NRL for automatic analysis of gamma-ray spectra from
                 germanium detectors.",
  acknowledgement = ack-nhfb,
  fjournal =     "Nuclear Instruments and Methods",
}


bibtype: article
filename: elefunt.bib
label: Risch:1979:APE
author: Robert H. Risch
title: Algebraic properties of the elementary functions of analysis
journal: j-AM-J-MATH
volume: 101
number: 4
pages: 743--759
year: 1979
CODEN: AJMAAN
ISSN: 0002-9327 (print), 1080-6377 (electronic) OR 00029327 (print), 10806377 (electronic)
ISSNL: 0002-9327 OR 00029327
MRclass: 12H05
MRnumber: 81b:12029
MRreviewer: J. L. Johnson
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
fjournal: American Journal of Mathematics
acknowledgement: ack-nhfb
rawauthor: Robert H. Risch
rawtitle: Algebraic properties of the elementary functions of analysis
entry:
@Article{Risch:1979:APE,
  author =       "Robert H. Risch",
  title =        "Algebraic properties of the elementary functions of
                 analysis",
  journal =      j-AM-J-MATH,
  volume =       "101",
  number =       "4",
  pages =        "743--759",
  year =         "1979",
  CODEN =        "AJMAAN",
  ISSN =         "0002-9327 (print), 1080-6377 (electronic)",
  ISSN-L =       "0002-9327",
  MRclass =      "12H05",
  MRnumber =     "81b:12029",
  MRreviewer =   "J. L. Johnson",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Journal of Mathematics",
}


bibtype: article
filename: elefunt.bib
label: Schulten:1979:AEC
author: Z. (or K. ??) Schulten and D. G. M. Anderson and R. G. Gordon
title: An Algorithm for the Evaluation of the Complex Airy Functions
journal: j-J-COMPUT-PHYS
volume: 31
number: 1
pages: 60--75
month: apr
monthnumber: 4
year: 1979
CODEN: JCTPAH
DOI: https://doi.org/10.1016/0021-9991(79)90062-7
ISSN: 0021-9991 (print), 1090-2716 (electronic) OR 00219991 (print), 10902716 (electronic)
ISSNL: 0021-9991 OR 00219991
bibdate: Sat Oct 30 10:34:34 2010
bibtimestamp: 2010.10.30 10:34:34 ???
fjournal: Journal of Computational Physics
remark: Fullerton: Simple formulae over the whole complex plane are presented.
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00219991/
rawauthor: Z. (or K. ??) Schulten and D. G. M. Anderson and R. G. Gordon
rawtitle: An Algorithm for the Evaluation of the Complex {Airy} Functions
entry:
@Article{Schulten:1979:AEC,
  author =       "Z. (or K. ??) Schulten and D. G. M. Anderson and R. G.
                 Gordon",
  title =        "An Algorithm for the Evaluation of the Complex {Airy}
                 Functions",
  journal =      j-J-COMPUT-PHYS,
  volume =       "31",
  number =       "1",
  pages =        "60--75",
  month =        apr,
  year =         "1979",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(79)90062-7",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Sat Oct 30 10:34:34 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1970.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
  remark =       "Fullerton: Simple formulae over the whole complex
                 plane are presented.",
}


bibtype: article
filename: elefunt.bib
label: Smith:1979:ALL
author: David A. Smith and William F. Ford
title: Acceleration of Linear and Logarithmic Convergence
journal: j-SIAM-J-NUMER-ANAL
volume: 16
number: 2
pages: 223--240
month: apr
monthnumber: 4
year: 1979
CODEN: SJNAAM
ISSN: 0036-1429 (print), 1095-7170 (electronic) OR 00361429 (print), 10957170 (electronic)
ISSNL: 0036-1429 OR 00361429
MRclass: 65B10
MRnumber: 82a:65012
bibdate: Fri Oct 16 06:57:22 MDT 1998
bibtimestamp: 1998.10.16 06:57:22 MDT
fjournal: SIAM Journal on Numerical Analysis
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sinum
rawauthor: David A. Smith and William F. Ford
rawtitle: Acceleration of Linear and Logarithmic Convergence
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib; JSTOR database

entry:
@Article{Smith:1979:ALL,
  author =       "David A. Smith and William F. Ford",
  title =        "Acceleration of Linear and Logarithmic Convergence",
  journal =      j-SIAM-J-NUMER-ANAL,
  volume =       "16",
  number =       "2",
  pages =        "223--240",
  month =        apr,
  year =         "1979",
  CODEN =        "SJNAAM",
  ISSN =         "0036-1429 (print), 1095-7170 (electronic)",
  ISSN-L =       "0036-1429",
  MRclass =      "65B10",
  MRnumber =     "82a:65012",
  bibdate =      "Fri Oct 16 06:57:22 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Numerical Analysis",
  journal-URL =  "http://epubs.siam.org/sinum",
}


bibtype: article
filename: elefunt.bib
label: Takemasa:1979:CFC
author: T. Takemasa and T. Tamura and H. H. Wolter
title: Coulomb Functions with Complex Angular Momenta
journal: j-COMP-PHYS-COMM
volume: 17
number: 4
pages: 351--355
month: jul
monthnumber: 7
year: 1979
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/0010-4655(79)90097-3
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Sat Oct 30 11:14:02 2010
bibtimestamp: 2010.10.30 11:14:02 ???
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: T. Takemasa and T. Tamura and H. H. Wolter
rawtitle: {Coulomb} Functions with Complex Angular Momenta
remark:
Fullerton: Description of program CCOULOM, which works only in the part of the $ (rho , eta ) $-plane where $ eta ^2 ll rho $ and $ | ell |^2 ll rho $.

entry:
@Article{Takemasa:1979:CFC,
  author =       "T. Takemasa and T. Tamura and H. H. Wolter",
  title =        "{Coulomb} Functions with Complex Angular Momenta",
  journal =      j-COMP-PHYS-COMM,
  volume =       "17",
  number =       "4",
  pages =        "351--355",
  month =        jul # "\slash " # aug,
  year =         "1979",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(79)90097-3",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Sat Oct 30 11:14:02 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
  remark =       "Fullerton: Description of program CCOULOM, which works
                 only in the part of the $ (\rho, \eta) $-plane where $
                 \eta^2 \ll \rho $ and $ | \ell |^2 \ll \rho $.",
}


bibtype: article
filename: elefunt.bib
label: Temme:1979:AAP
author: N. M. Temme
journal: j-J-COMPUT-PHYS
volume: 32
number: 2
pages: 270--279
month: aug
monthnumber: 8
year: 1979
CODEN: JCTPAH
DOI: https://doi.org/10.1016/0021-9991(79)90134-7
ISSN: 0021-9991 (print), 1090-2716 (electronic) OR 00219991 (print), 10902716 (electronic)
ISSNL: 0021-9991 OR 00219991
bibdate: Sat Oct 30 11:23:13 2010
bibtimestamp: 2010.10.30 11:23:13 ???
fjournal: Journal of Computational Physics
remark: Fullerton: An adjustable-accuracy 100 line Algol procedure is discussed.
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00219991/
rawauthor: N. M. Temme
title:
An Algorithm with ALGOL 60 Program for the Computation of the Zeros of Ordinary Bessel Functions and those of their Derivatives

rawtitle:
An Algorithm with {ALGOL 60} Program for the Computation of the Zeros of Ordinary {Bessel} Functions and those of their Derivatives

entry:
@Article{Temme:1979:AAP,
  author =       "N. M. Temme",
  title =        "An Algorithm with {ALGOL 60} Program for the
                 Computation of the Zeros of Ordinary {Bessel} Functions
                 and those of their Derivatives",
  journal =      j-J-COMPUT-PHYS,
  volume =       "32",
  number =       "2",
  pages =        "270--279",
  month =        aug,
  year =         "1979",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(79)90134-7",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Sat Oct 30 11:23:13 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1970.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
  remark =       "Fullerton: An adjustable-accuracy 100 line Algol
                 procedure is discussed.",
}


bibtype: article
filename: elefunt.bib
label: Temme:1979:AEI
author: N. M. Temme
title: The asymptotic expansion of the incomplete gamma functions
journal: j-SIAM-J-MATH-ANA
volume: 10
number: 4
pages: 757--766
month: jul
monthnumber: 7
year: 1979
CODEN: SJMAAH
ISSN: 0036-1410 (print), 1095-7154 (electronic) OR 00361410 (print), 10957154 (electronic)
ISSNL: 0036-1410 OR 00361410
MRclass: 33A15
MRnumber: 80i:33002
MRreviewer: E. Rieksti\lfhook n{\v{s}}
bibdate: Sun Nov 28 19:22:16 MST 2010
bibtimestamp: 2010.11.28 19:22:16 MST
fjournal: SIAM Journal on Mathematical Analysis
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sima
rawauthor: N. M. Temme
rawtitle: The asymptotic expansion of the incomplete gamma functions
bibsource:
http://epubs.siam.org/sam-bin/dbq/toc/SIMA/10/4; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/siamjmathana.bib

entry:
@Article{Temme:1979:AEI,
  author =       "N. M. Temme",
  title =        "The asymptotic expansion of the incomplete gamma
                 functions",
  journal =      j-SIAM-J-MATH-ANA,
  volume =       "10",
  number =       "4",
  pages =        "757--766",
  month =        jul,
  year =         "1979",
  CODEN =        "SJMAAH",
  ISSN =         "0036-1410 (print), 1095-7154 (electronic)",
  ISSN-L =       "0036-1410",
  MRclass =      "33A15",
  MRnumber =     "80i:33002",
  MRreviewer =   "E. Rieksti\lfhook n{\v{s}}",
  bibdate =      "Sun Nov 28 19:22:16 MST 2010",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMA/10/4;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjmathana.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Mathematical Analysis",
  journal-URL =  "http://epubs.siam.org/sima",
}


bibtype: article
filename: elefunt.bib
label: Terras:1979:DIG
author: Riho Terras
title: The determination of incomplete gamma functions through analytic integration
journal: j-J-COMPUT-PHYS
volume: 31
number: 1
pages: 146--151
month: apr
monthnumber: 4
year: 1979
CODEN: JCTPAH
DOI: https://doi.org/10.1016/0021-9991(79)90066-4
ISSN: 0021-9991 (print), 1090-2716 (electronic) OR 00219991 (print), 10902716 (electronic)
ISSNL: 0021-9991 OR 00219991
bibdate: Sun Jan 1 09:15:33 MST 2012
bibtimestamp: 2012.01.01 09:15:33 MST
URL: http://www.sciencedirect.com/science/article/pii/0021999179900664
fjournal: Journal of Computational Physics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00219991/
rawauthor: Riho Terras
rawtitle: The determination of incomplete gamma functions through analytic integration
entry:
@Article{Terras:1979:DIG,
  author =       "Riho Terras",
  title =        "The determination of incomplete gamma functions
                 through analytic integration",
  journal =      j-J-COMPUT-PHYS,
  volume =       "31",
  number =       "1",
  pages =        "146--151",
  month =        apr,
  year =         "1979",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(79)90066-4",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Sun Jan 1 09:15:33 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1970.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0021999179900664",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}


bibtype: article
filename: elefunt.bib
label: Thacher:1979:NBR
author: Henry C. Thacher, Jr.
title: New Backward Recurrences for Bessel Functions
journal: j-MATH-COMPUT
volume: 33
number: 146
pages: 744--764
month: apr
monthnumber: 4
year: 1979
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 65D20 (33A40)
MRnumber: 81b:65019
MRreviewer: R. G. Langebartel
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
keywords: backward recurrences; Bessel functions; converges
acknowledgement: ack-nhfb
classcodes: C1120 (Mathematical analysis)
corpsource: Dept. of Computer Sci., Univ. of Kentucky, Lexington, KY, USA
journalURL: http://www.ams.org/mcom/
treatment: N New Development; T Theoretical or Mathematical
rawauthor: Henry C. {Thacher, Jr.}
rawtitle: New Backward Recurrences for {Bessel} Functions
entry:
@Article{Thacher:1979:NBR,
  author =       "Henry C. {Thacher, Jr.}",
  title =        "New Backward Recurrences for {Bessel} Functions",
  journal =      j-MATH-COMPUT,
  volume =       "33",
  number =       "146",
  pages =        "744--764",
  month =        apr,
  year =         "1979",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65D20 (33A40)",
  MRnumber =     "81b:65019",
  MRreviewer =   "R. G. Langebartel",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "C1120 (Mathematical analysis)",
  corpsource =   "Dept. of Computer Sci., Univ. of Kentucky, Lexington,
                 KY, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "backward recurrences; Bessel functions; converges",
  treatment =    "N New Development; T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Brent:1980:SNA
author: Richard P. Brent and Edwin M. McMillan
title: Some new algorithms for high-precision computation of Euler's constant
journal: j-MATH-COMPUT
volume: 34
number: 149
pages: 305--312
month: jan
monthnumber: 1
year: 1980
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 10-04 (10A40 68C05)
MRnumber: 82g:10002
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
keywords: Bessel functions; computation; Euler's constant; function evaluation; high precision
acknowledgement: ack-nhfb
classcodes: B0290D (Functional analysis); C4120 (Functional analysis)
corpsource: Univ. of California, Berkeley, CA, USA
journalURL: http://www.ams.org/mcom/
treatment: N New Development; T Theoretical or Mathematical
rawauthor: Richard P. Brent and Edwin M. McMillan
rawtitle: Some new algorithms for high-precision computation of {Euler}'s constant
remark:
Fullerton: Calculation to 30,100 places is discussed, but only a 3-digit value appears in the paper.

entry:
@Article{Brent:1980:SNA,
  author =       "Richard P. Brent and Edwin M. McMillan",
  title =        "Some new algorithms for high-precision computation of
                 {Euler}'s constant",
  journal =      j-MATH-COMPUT,
  volume =       "34",
  number =       "149",
  pages =        "305--312",
  month =        jan,
  year =         "1980",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "10-04 (10A40 68C05)",
  MRnumber =     "82g:10002",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "B0290D (Functional analysis); C4120 (Functional
                 analysis)",
  corpsource =   "Univ. of California, Berkeley, CA, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Bessel functions; computation; Euler's constant;
                 function evaluation; high precision",
  remark =       "Fullerton: Calculation to 30,100 places is discussed,
                 but only a 3-digit value appears in the paper.",
  treatment =    "N New Development; T Theoretical or Mathematical",
}


bibtype: inproceedings
filename: elefunt.bib
label: Brent:1980:UAE
author: R. P. Brent
title: Unrestricted Algorithms for Elementary and Special Functions
crossref: Lavington:1980:IPP
pages: 613--619
year: 1980
bibdate: Thu Sep 01 11:55:31 1994
bibsource: garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.09.01 11:55:31 ???
URL: http://maths-people.anu.edu.au/~brent/pub/pub052.html
acknowledgement: ack-nj
rawauthor: R. P. Brent
rawtitle: Unrestricted Algorithms for Elementary and Special Functions
remark:
From the author's Web site: Errata for original version:par Page 615, remove the absolute value signs in equation (13) and the following paragraph (x should be large and positive here).par Page 616, second half of equation (26): insert a minus sign after the equals sign.par Page 617, equation (39): delete `` / j ! ''.par Page 617, equation (42): the assumption ``j < k'' should be added. Also, the contour C needs to be enlarged slightly.par Page 617, left-hand-side of equation (44): replace ``Sj,k'' by ``S2j,k''.par Page 617, ten lines after equation (44): replace ``O(jn2)'' by ``O(j2n)''.

entry:
@InProceedings{Brent:1980:UAE,
  author =       "R. P. Brent",
  title =        "Unrestricted Algorithms for Elementary and Special
                 Functions",
  crossref =     "Lavington:1980:IPP",
  pages =        "613--619",
  year =         "1980",
  bibdate =      "Thu Sep 01 11:55:31 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://maths-people.anu.edu.au/~brent/pub/pub052.html",
  acknowledgement = ack-nj,
  remark =       "From the author's Web site: Errata for original
                 version:\par Page 615, remove the absolute value signs
                 in equation (13) and the following paragraph (x should
                 be large and positive here).\par

                 Page 616, second half of equation (26): insert a minus
                 sign after the equals sign.\par

                 Page 617, equation (39): delete `` / j ! ''.\par

                 Page 617, equation (42): the assumption ``j < k''
                 should be added. Also, the contour C needs to be
                 enlarged slightly.\par

                 Page 617, left-hand-side of equation (44): replace
                 ``Sj,k'' by ``S2j,k''.\par

                 Page 617, ten lines after equation (44): replace
                 ``O(jn2)'' by ``O(j2n)''.",
}


bibtype: article
filename: elefunt.bib
label: Brezinski:1980:GEA
author: C. Brezinski
title: A general extrapolation algorithm
journal: j-NUM-MATH
volume: 35
number: 2
pages: 175--187
month: jun
monthnumber: 6
year: 1980
CODEN: NUMMA7
ISSN: 0029-599X (print), 0945-3245 (electronic) OR 0029599X (print), 09453245 (electronic)
ISSNL: 0029-599X OR 0029599X
MRclass: 65B05
MRnumber: 81j:65015
MRreviewer: L. Fox
bibdate: Mon May 26 11:49:34 MDT 1997
bibtimestamp: 1997.05.26 11:49:34 MDT
fjournal: Numerische Mathematik
acknowledgement: ack-nhfb
corpsource: UER IEEA, Univ. de Lille 1, Villeneuve d'Ascq, France
journalURL: http://link.springer.com/journal/211
treatment: T Theoretical or Mathematical
rawauthor: C. Brezinski
rawtitle: A general extrapolation algorithm
keywords:
convergence acceleration; extrapolation; extrapolation algorithm; linear extrapolation; rational extrapolation; recursive algorithm; sequence transformations

entry:
@Article{Brezinski:1980:GEA,
  author =       "C. Brezinski",
  title =        "A general extrapolation algorithm",
  journal =      j-NUM-MATH,
  volume =       "35",
  number =       "2",
  pages =        "175--187",
  month =        jun,
  year =         "1980",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "65B05",
  MRnumber =     "81j:65015",
  MRreviewer =   "L. Fox",
  bibdate =      "Mon May 26 11:49:34 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/nummath.bib",
  acknowledgement = ack-nhfb,
  classification = "C4130 (Interpolation and function approximation)",
  corpsource =   "UER IEEA, Univ. de Lille 1, Villeneuve d'Ascq,
                 France",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "convergence acceleration; extrapolation; extrapolation
                 algorithm; linear extrapolation; rational
                 extrapolation; recursive algorithm; sequence
                 transformations",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Char:1980:SCF
author: Bruce W. Char
title: On Stieltjes' continued fraction for the gamma function
journal: j-MATH-COMPUT
volume: 34
number: 150
pages: 547--551
month: apr
monthnumber: 4
year: 1980
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 65A05 (65D20)
MRnumber: 81b:65008
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
remark: Fullerton: The first 41 coefficients to 40 digits are given.
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Bruce W. Char
rawtitle: On {Stieltjes}' continued fraction for the gamma function
entry:
@Article{Char:1980:SCF,
  author =       "Bruce W. Char",
  title =        "On {Stieltjes}' continued fraction for the gamma
                 function",
  journal =      j-MATH-COMPUT,
  volume =       "34",
  number =       "150",
  pages =        "547--551",
  month =        apr,
  year =         "1980",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65A05 (65D20)",
  MRnumber =     "81b:65008",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  remark =       "Fullerton: The first 41 coefficients to 40 digits are
                 given.",
}


bibtype: article
filename: elefunt.bib
label: Clenshaw:1980:UAE
author: C. W. Clenshaw and Frank W. J. Olver
title: An unrestricted algorithm for the exponential function
journal: j-SIAM-J-NUMER-ANAL
volume: 17
number: 2
pages: 310--331
month: apr
monthnumber: 4
year: 1980
CODEN: SJNAAM
DOI: https://doi.org/10.1137/0717026
ISSN: 0036-1429 (print), 1095-7170 (electronic) OR 00361429 (print), 10957170 (electronic)
ISSNL: 0036-1429 OR 00361429
MRclass: 65D20
MRnumber: 567276
MRreviewer: A. M. Cohen
bibdate: Sun Nov 12 06:18:24 2023
bibtimestamp: 2023.11.12 06:18:24 ???
fjournal: SIAM Journal on Numerical Analysis
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sinum
rawauthor: C. W. Clenshaw and Frank W. J. Olver
rawtitle: An unrestricted algorithm for the exponential function
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/c/clenshaw-charles-w.bib; https://www.math.utah.edu/pub/bibnet/authors/o/olver-frank-w-j.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

abstract:
An algorithm is presented for the computation of the exponential function of real argument. There are no restrictions on the range of the argument or on the precision that may be demanded in the results.

authordates:
Charles William Clenshaw (15 March 1926--23 September 2004); Frank William John Olver (15 December 1924--23 April 2013)

rawabstract:
An algorithm is presented for the computation of the exponential function of real argument. There are no restrictions on the range of the argument or on the precision that may be demanded in the results.

entry:
@Article{Clenshaw:1980:UAE,
  author =       "C. W. Clenshaw and Frank W. J. Olver",
  title =        "An unrestricted algorithm for the exponential
                 function",
  journal =      j-SIAM-J-NUMER-ANAL,
  volume =       "17",
  number =       "2",
  pages =        "310--331",
  month =        apr,
  year =         "1980",
  CODEN =        "SJNAAM",
  DOI =          "https://doi.org/10.1137/0717026",
  ISSN =         "0036-1429 (print), 1095-7170 (electronic)",
  ISSN-L =       "0036-1429",
  MRclass =      "65D20",
  MRnumber =     "567276",
  MRreviewer =   "A. M. Cohen",
  bibdate =      "Sun Nov 12 06:18:24 2023",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/clenshaw-charles-w.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/o/olver-frank-w-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "An algorithm is presented for the computation of the
                 exponential function of real argument. There are no
                 restrictions on the range of the argument or on the
                 precision that may be demanded in the results.",
  acknowledgement = ack-nhfb,
  author-dates = "Charles William Clenshaw (15 March 1926--23 September
                 2004); Frank William John Olver (15 December 1924--23
                 April 2013)",
  fjournal =     "SIAM Journal on Numerical Analysis",
  journal-URL =  "http://epubs.siam.org/sinum",
}


bibtype: book
filename: elefunt.bib
label: Cody:1980:SME
author: William J. Cody, Jr. and William Waite
title: Software Manual for the Elementary Functions
publisher: pub-PH
address: pub-PH:adr
pages: x + 269
year: 1980
ISBN: 0-13-822064-6 OR 0138220646
ISBN13: 978-0-13-822064-8 OR 9780138220648
LCCN: QA331 .C635 1980
bibdate: Tue Dec 14 23:28:38 1993
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/master.bib
bibtimestamp: 1993.12.14 23:28:38 ???
acknowledgement: ack-nhfb
rawauthor: William J. {Cody, Jr.} and William Waite
rawtitle: Software Manual for the Elementary Functions
TOC:
Preface / ix 1. Introduction / 1 2. Preliminaries / 3 3. Performance Testing / 11 4. SQRT / 17 a. General Discussion / 17 b. Flow Chart for SQRT(X) / 18 c. Implementation Notes, Non-Decimal Fixed-Point Machines / 19 d. Implementation Notes, Binary Floating-Point Machines / 23 e. Implementation Notes, Non-Binary Floating-Point Machines / 25 f. Testing / 28 5. ALOG/ALOG10 / 35 a. General Discussion / 35 b. Flow Chart for ALOG(X)/ALOG10(X) / 37 c. Implementation Notes, Non-Decimal Fixed-Point Machines / 38 d. Implementation Notes, Non-Decimal Floating-Point Machines / 42 e. Implementation Notes, Decimal Floating-Point Machines / 46 f. Testing / 49 6. EXP / 60 a. General Discussion / 60 b. Flow Chart for EXP(X) / 62 c. Implementation Notes, Non-Decimal Fixed-Point Machines / 63 d. Implementation Notes, Non-Decimal Floating-Point Machines / 67 e. Implementation Notes, Decimal Floating-Point Machines / 71 f. Testing / 75 7. POWER (**) / 84 a. General Discussion / 84 b. Flow Chart for POWER(X,Y) / 88 c. Implementation Notes, Non-Decimal Fixed-Point Machines / 90 d. Implementation Notes, Non-Decimal Floating-Point Machines / 97 e. Implementation Notes, Decimal Floating-Point Machines / 106 f. Testing / 113 8. SIN/COS / 125 a. General Discussion / 125 b. Flow Chart for SIN(X)/COS(X) / 127 c. Implementation Notes, Non-Decimal Fixed-Point Machines / 129 d. Implementation Notes, All Floating-Point Machines / 134 e. Testing / 139 9. TAN/COT / 150 a. General Discussion / 150 b. Flow Chart for TAN(X)/COTAN(X) / 152 c. Implementation Notes, Non-Decimal Fixed-Point Machines / 154 d. Implementation Notes, All Floating-Point Machines / 159 e. Testing / 164 10. ASIN/ACOS / 174 a. General Discuss i on / 174 b. Flow Chart for AS IN(X)/ACOS(X) / 176 c. Implementation Not es, Non-Decimal Fixed-Point Machines / 177 d. Implementation Notes, All Floating-Point Machines / 181 e. Testing / 185 11. ATAN/ATAN2 / 194 a. General Discussion / 194 b. Flow Chart for ATAN(X)/ATAN2(V,U) / 196 c. Implementation Notes, Non-Decimal Fixed-Point Machines / 198 d. Implementation Notes, All Floating-Point Machines / 203 e. Testing / 207 12. SINH/COSH / 217 a. General Discussion / 217 b. Flow Chart for SINH(X)/COSH(X) / 220 c. Implementation Notes, Non-Decimal Fixed-Point Machines / 221 d. Implementation Notes, All Floating-Point Machines / 225 e. Testing / 229

shortTOC:
Preface / ix 1. Introduction / 1 2. Preliminaries / 3 3. Performance Testing / 11 4. SQRT / 17 5. ALOG/ALOG10 / 35 6. EXP / 60 7. POWER (**) / 84 8. SIN/COS / 125 9. TAN/COT / 150 10. ASIN/ACOS / 174 11. ATAN/ATAN2 / 194 12. SINH/COSH / 217

rawshortTOC:
Preface / ix \\ 1. Introduction / 1 \\ 2. Preliminaries / 3 \\ 3. Performance Testing / 11 \\ 4. SQRT / 17 \\ 5. ALOG/ALOG10 / 35 \\ 6. EXP / 60 \\ 7. POWER (**) / 84 \\ 8. SIN/COS / 125 \\ 9. TAN/COT / 150 \\ 10. ASIN/ACOS / 174 \\ 11. ATAN/ATAN2 / 194 \\ 12. SINH/COSH / 217

rawTOC:
Preface / ix \\ 1. Introduction / 1 \\ 2. Preliminaries / 3 \\ 3. Performance Testing / 11 \\ 4. SQRT / 17 \\ a. General Discussion / 17 \\ b. Flow Chart for SQRT(X) / 18 \\ c. Implementation Notes, Non-Decimal Fixed-Point Machines / 19 \\ d. Implementation Notes, Binary Floating-Point Machines / 23 \\ e. Implementation Notes, Non-Binary Floating-Point Machines / 25 \\ f. Testing / 28 \\ 5. ALOG/ALOG10 / 35 \\ a. General Discussion / 35 \\ b. Flow Chart for ALOG(X)/ALOG10(X) / 37 \\ c. Implementation Notes, Non-Decimal Fixed-Point Machines / 38 \\ d. Implementation Notes, Non-Decimal Floating-Point Machines / 42 \\ e. Implementation Notes, Decimal Floating-Point Machines / 46 \\ f. Testing / 49 \\ 6. EXP / 60 \\ a. General Discussion / 60 \\ b. Flow Chart for EXP(X) / 62 \\ c. Implementation Notes, Non-Decimal Fixed-Point Machines / 63 \\ d. Implementation Notes, Non-Decimal Floating-Point Machines / 67 \\ e. Implementation Notes, Decimal Floating-Point Machines / 71 \\ f. Testing / 75 \\ 7. POWER (**) / 84 \\ a. General Discussion / 84 \\ b. Flow Chart for POWER(X,Y) / 88 \\ c. Implementation Notes, Non-Decimal Fixed-Point Machines / 90 \\ d. Implementation Notes, Non-Decimal Floating-Point Machines / 97 \\ e. Implementation Notes, Decimal Floating-Point Machines / 106 \\ f. Testing / 113 \\ 8. SIN/COS / 125 \\ a. General Discussion / 125 \\ b. Flow Chart for SIN(X)/COS(X) / 127 \\ c. Implementation Notes, Non-Decimal Fixed-Point Machines / 129 \\ d. Implementation Notes, All Floating-Point Machines / 134 \\ e. Testing / 139 \\ 9. TAN/COT / 150 \\ a. General Discussion / 150 \\ b. Flow Chart for TAN(X)/COTAN(X) / 152 \\ c. Implementation Notes, Non-Decimal Fixed-Point Machines / 154 \\ d. Implementation Notes, All Floating-Point Machines / 159 \\ e. Testing / 164 \\ 10. ASIN/ACOS / 174 \\ a. General Discuss i on / 174 \\ b. Flow Chart for AS IN(X)/ACOS(X) / 176 \\ c. Implementation Not es, Non-Decimal Fixed-Point Machines / 177 \\ d. Implementation Notes, All Floating-Point Machines / 181 \\ e. Testing / 185 \\ 11. ATAN/ATAN2 / 194 \\ a. General Discussion / 194 \\ b. Flow Chart for ATAN(X)/ATAN2(V,U) / 196 \\ c. Implementation Notes, Non-Decimal Fixed-Point Machines / 198 \\ d. Implementation Notes, All Floating-Point Machines / 203 \\ e. Testing / 207 \\ 12. SINH/COSH / 217 \\ a. General Discussion / 217 \\ b. Flow Chart for SINH(X)/COSH(X) / 220 \\ c. Implementation Notes, Non-Decimal Fixed-Point Machines / 221 \\ d. Implementation Notes, All Floating-Point Machines / 225 \\ e. Testing / 229

entry:
@Book{Cody:1980:SME,
  author =       "William J. {Cody, Jr.} and William Waite",
  title =        "Software Manual for the Elementary Functions",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "x + 269",
  year =         "1980",
  ISBN =         "0-13-822064-6",
  ISBN-13 =      "978-0-13-822064-8",
  LCCN =         "QA331 .C635 1980",
  bibdate =      "Tue Dec 14 23:28:38 1993",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  acknowledgement = ack-nhfb,
  shorttableofcontents = "Preface / ix \\
                 1. Introduction / 1 \\
                 2. Preliminaries / 3 \\
                 3. Performance Testing / 11 \\
                 4. SQRT / 17 \\
                 5. ALOG/ALOG10 / 35 \\
                 6. EXP / 60 \\
                 7. POWER (**) / 84 \\
                 8. SIN/COS / 125 \\
                 9. TAN/COT / 150 \\
                 10. ASIN/ACOS / 174 \\
                 11. ATAN/ATAN2 / 194 \\
                 12. SINH/COSH / 217",
  tableofcontents = "Preface / ix \\
                 1. Introduction / 1 \\
                 2. Preliminaries / 3 \\
                 3. Performance Testing / 11 \\
                 4. SQRT / 17 \\
                 a. General Discussion / 17 \\
                 b. Flow Chart for SQRT(X) / 18 \\
                 c. Implementation Notes, Non-Decimal Fixed-Point
                 Machines / 19 \\
                 d. Implementation Notes, Binary Floating-Point Machines
                 / 23 \\
                 e. Implementation Notes, Non-Binary Floating-Point
                 Machines / 25 \\
                 f. Testing / 28 \\
                 5. ALOG/ALOG10 / 35 \\
                 a. General Discussion / 35 \\
                 b. Flow Chart for ALOG(X)/ALOG10(X) / 37 \\
                 c. Implementation Notes, Non-Decimal Fixed-Point
                 Machines / 38 \\
                 d. Implementation Notes, Non-Decimal Floating-Point
                 Machines / 42 \\
                 e. Implementation Notes, Decimal Floating-Point
                 Machines / 46 \\
                 f. Testing / 49 \\
                 6. EXP / 60 \\
                 a. General Discussion / 60 \\
                 b. Flow Chart for EXP(X) / 62 \\
                 c. Implementation Notes, Non-Decimal Fixed-Point
                 Machines / 63 \\
                 d. Implementation Notes, Non-Decimal Floating-Point
                 Machines / 67 \\
                 e. Implementation Notes, Decimal Floating-Point
                 Machines / 71 \\
                 f. Testing / 75 \\
                 7. POWER (**) / 84 \\
                 a. General Discussion / 84 \\
                 b. Flow Chart for POWER(X,Y) / 88 \\
                 c. Implementation Notes, Non-Decimal Fixed-Point
                 Machines / 90 \\
                 d. Implementation Notes, Non-Decimal Floating-Point
                 Machines / 97 \\
                 e. Implementation Notes, Decimal Floating-Point
                 Machines / 106 \\
                 f. Testing / 113 \\
                 8. SIN/COS / 125 \\
                 a. General Discussion / 125 \\
                 b. Flow Chart for SIN(X)/COS(X) / 127 \\
                 c. Implementation Notes, Non-Decimal Fixed-Point
                 Machines / 129 \\
                 d. Implementation Notes, All Floating-Point Machines /
                 134 \\
                 e. Testing / 139 \\
                 9. TAN/COT / 150 \\
                 a. General Discussion / 150 \\
                 b. Flow Chart for TAN(X)/COTAN(X) / 152 \\
                 c. Implementation Notes, Non-Decimal Fixed-Point
                 Machines / 154 \\
                 d. Implementation Notes, All Floating-Point Machines /
                 159 \\
                 e. Testing / 164 \\
                 10. ASIN/ACOS / 174 \\
                 a. General Discuss i on / 174 \\
                 b. Flow Chart for AS IN(X)/ACOS(X) / 176 \\
                 c. Implementation Not es, Non-Decimal Fixed-Point
                 Machines / 177 \\
                 d. Implementation Notes, All Floating-Point Machines /
                 181 \\
                 e. Testing / 185 \\
                 11. ATAN/ATAN2 / 194 \\
                 a. General Discussion / 194 \\
                 b. Flow Chart for ATAN(X)/ATAN2(V,U) / 196 \\
                 c. Implementation Notes, Non-Decimal Fixed-Point
                 Machines / 198 \\
                 d. Implementation Notes, All Floating-Point Machines /
                 203 \\
                 e. Testing / 207 \\
                 12. SINH/COSH / 217 \\
                 a. General Discussion / 217 \\
                 b. Flow Chart for SINH(X)/COSH(X) / 220 \\
                 c. Implementation Notes, Non-Decimal Fixed-Point
                 Machines / 221 \\
                 d. Implementation Notes, All Floating-Point Machines /
                 225 \\
                 e. Testing / 229",
}


bibtype: article
filename: elefunt.bib
label: Coleman:1980:FSB
author: J. P. Coleman
title: A Fortran subroutine for the Bessel function $ J_n(x) $ of order $0$ to $ 10 $
journal: j-COMP-PHYS-COMM
volume: 21
number: 1
pages: 109--118
day: 1
month: dec
monthnumber: 12
year: 1980
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/0010-4655(80)90080-6
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Mon Feb 13 06:01:19 MST 2012
bibtimestamp: 2012.02.13 06:01:19 MST
URL: http://www.sciencedirect.com/science/article/pii/0010465580900806
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: J. P. Coleman
rawtitle: A {Fortran} subroutine for the {Bessel} function {$ J_n(x) $} of order $0$ to $ 10 $
bibsource:
https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fortran1.bib

entry:
@Article{Coleman:1980:FSB,
  author =       "J. P. Coleman",
  title =        "A {Fortran} subroutine for the {Bessel} function {$
                 J_n(x) $} of order $0$ to $ 10 $",
  journal =      j-COMP-PHYS-COMM,
  volume =       "21",
  number =       "1",
  pages =        "109--118",
  day =          "1",
  month =        dec,
  year =         "1980",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(80)90080-6",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Feb 13 06:01:19 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fortran1.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0010465580900806",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}


bibtype: article
filename: elefunt.bib
label: Delahaye:1980:RNA
author: J. P. Delahaye and B. Germain-Bonne
journal: j-NUM-MATH
volume: 35
number: 4
pages: 443--457
month: nov
monthnumber: 11
year: 1980
CODEN: NUMMA7
ISSN: 0029-599X (print), 0945-3245 (electronic) OR 0029599X (print), 09453245 (electronic)
ISSNL: 0029-599X OR 0029599X
MRclass: 65B99 (40A99)
MRnumber: 81k:65007
MRreviewer: Claude Brezinski
bibdate: Mon May 26 11:49:34 MDT 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.05.26 11:49:34 MDT
fjournal: Numerische Mathematik
language: French
acknowledgement: ack-nhfb
corpsource: Univ. des Sci. et Tech. de Lille I, Villeneuve d'Ascq, France
journalURL: http://link.springer.com/journal/211
treatment: T Theoretical or Mathematical
rawauthor: J. P. Delahaye and B. Germain-Bonne
title:
Resultats negatifs en acceleration de la convergence. (French) [Negative results in convergence acceleration]

keywords:
acceleration; algorithm; approximation theory; computational complexity; convergence; convergence acceleration; convergence of numerical methods

rawtitle:
{R}{\'e}sultats n{\'e}gatifs en acc{\'e}l{\'e}ration de la convergence. ({French}) [{Negative} results in convergence acceleration]

entry:
@Article{Delahaye:1980:RNA,
  author =       "J. P. Delahaye and B. Germain-Bonne",
  title =        "{R}{\'e}sultats n{\'e}gatifs en acc{\'e}l{\'e}ration
                 de la convergence. ({French}) [{Negative} results in
                 convergence acceleration]",
  journal =      j-NUM-MATH,
  volume =       "35",
  number =       "4",
  pages =        "443--457",
  month =        nov,
  year =         "1980",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "65B99 (40A99)",
  MRnumber =     "81k:65007",
  MRreviewer =   "Claude Brezinski",
  bibdate =      "Mon May 26 11:49:34 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  classification = "C4130 (Interpolation and function approximation);
                 C4240 (Programming and algorithm theory)",
  corpsource =   "Univ. des Sci. et Tech. de Lille I, Villeneuve d'Ascq,
                 France",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "acceleration; algorithm; approximation theory;
                 computational complexity; convergence; convergence
                 acceleration; convergence of numerical methods",
  language =     "French",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Ditkin:1980:CSF
author: V. A. Ditkin and K. A. Karpov and M. K. Kerimov
title: The computation of special functions
journal: j-USSR-COMP-MATH-MATH-PHYS
volume: 20
number: 5
pages: 3--12
year: 1980
CODEN: CMMPA9
ISSN: 0041-5553, 0502-9902 OR 00415553, 05029902
ISSNL: 0041-5553 OR 00415553
bibdate: Fri Nov 8 18:01:57 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2002.11.08 18:01:57 MST
fjournal: U.S.S.R. Computational Mathematics and Mathematical Physics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00415553
journalabr: USSR Comput. Math. Math. Phys
rawauthor: V. A. Ditkin and K. A. Karpov and M. K. Kerimov
rawtitle: The computation of special functions
subject:
G. Mathematics of Computing; G.2 DISCRETE MATHEMATICS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS

entry:
@Article{Ditkin:1980:CSF,
  author =       "V. A. Ditkin and K. A. Karpov and M. K. Kerimov",
  title =        "The computation of special functions",
  journal =      j-USSR-COMP-MATH-MATH-PHYS,
  volume =       "20",
  number =       "5",
  pages =        "3--12",
  year =         "1980",
  CODEN =        "CMMPA9",
  ISSN =         "0041-5553, 0502-9902",
  ISSN-L =       "0041-5553",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  catcode =      "G.2.1; G.1.2",
  CRclass =      "G.2.1 Combinatorics; G.2.1 Generating functions; G.1.2
                 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, DISCRETE MATHEMATICS,
                 Combinatorics, Generating functions; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation,
                 Elementary function approximation",
  fjournal =     "U.S.S.R. Computational Mathematics and Mathematical
                 Physics",
  genterm =      "algorithms; design",
  guideno =      "09092",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00415553",
  journalabr =   "USSR Comput. Math. Math. Phys",
  jrldate =      "1980",
  subject =      "G. Mathematics of Computing; G.2 DISCRETE MATHEMATICS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}


bibtype: article
filename: elefunt.bib
label: Eckhardt:1980:AWE
author: Ulrich Eckhardt
title: Algorithm 549: Weierstrass' Elliptic Functions [S21]
journal: j-TOMS
volume: 6
number: 1
pages: 112--120
month: mar
monthnumber: 3
year: 1980
CODEN: ACMSCU
DOI: https://doi.org/10.1145/355873.355884
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Mon Aug 29 10:31:24 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.08.29 10:31:24 ???
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: Weierstrass' elliptic functions
remark: Fullerton: A complex FORTRAN algorithm with accuracy down to $ 10^-18 $ is given
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Ulrich Eckhardt
rawtitle: {Algorithm 549}: {Weierstrass}' Elliptic Functions [{S21}]
entry:
@Article{Eckhardt:1980:AWE,
  author =       "Ulrich Eckhardt",
  title =        "{Algorithm 549}: {Weierstrass}' Elliptic Functions
                 [{S21}]",
  journal =      j-TOMS,
  volume =       "6",
  number =       "1",
  pages =        "112--120",
  month =        mar,
  year =         "1980",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355873.355884",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 29 10:31:24 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Weierstrass' elliptic functions",
  remark =       "Fullerton: A complex FORTRAN algorithm with accuracy
                 down to $ 10^{-18} $ is given",
}


bibtype: article
filename: elefunt.bib
label: Fransen:1980:HPV
author: Arne Fransen and Staffan Wrigge
title: High-precision values of the gamma function and of some related coefficients
journal: j-MATH-COMPUT
volume: 34
number: 150
pages: 553--566
month: apr
monthnumber: 4
year: 1980
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 65A05 (65D20)
MRnumber: 81f:65004
MRreviewer: F. W. J. Olver
bibdate: Sat Apr 01 10:12:58 2000
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 2000.04.01 10:12:58 ???
note: See addendum and corrigendum cite Fransen:1981:ACH.
fjournal: Mathematics of Computation
remark: Fullerton: 80D values of coefficients in the Taylor series for $ Gamma ^m(s + x) $ are given.
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Arne Frans{\'e}n and Staffan Wrigge
rawnote: See addendum and corrigendum \cite{Fransen:1981:ACH}.
rawtitle: High-precision values of the gamma function and of some related coefficients
entry:
@Article{Fransen:1980:HPV,
  author =       "Arne Frans{\'e}n and Staffan Wrigge",
  title =        "High-precision values of the gamma function and of
                 some related coefficients",
  journal =      j-MATH-COMPUT,
  volume =       "34",
  number =       "150",
  pages =        "553--566",
  month =        apr,
  year =         "1980",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65A05 (65D20)",
  MRnumber =     "81f:65004",
  MRreviewer =   "F. W. J. Olver",
  bibdate =      "Sat Apr 01 10:12:58 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  note =         "See addendum and corrigendum
                 \cite{Fransen:1981:ACH}.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  remark =       "Fullerton: 80D values of coefficients in the Taylor
                 series for $ \Gamma^m(s + x) $ are given.",
}


bibtype: techreport
filename: elefunt.bib
label: Fullerton:1980:BEM
author: L. W. Fullerton
title: A Bibliography on the Evaluation of Mathematical Functions
type: Technical report
number: TM 80-1274-4 and CSTR 86
institution: inst-ATT-BELL
address: inst-ATT-BELL:adr
pages: 553--566
month: sep
monthnumber: 9
year: 1980
bibdate: Sat Feb 05 17:39:14 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.02.05 17:39:14 ???
acknowledgement: ack-nhfb
rawauthor: L. W. Fullerton
rawtitle: A Bibliography on the Evaluation of Mathematical Functions
entry:
@TechReport{Fullerton:1980:BEM,
  author =       "L. W. Fullerton",
  title =        "A Bibliography on the Evaluation of Mathematical
                 Functions",
  type =         "Technical report",
  number =       "TM 80-1274-4 and CSTR 86",
  institution =  inst-ATT-BELL,
  address =      inst-ATT-BELL:adr,
  month =        sep,
  year =         "1980",
  bibdate =      "Sat Feb 05 17:39:14 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Gargantini:1980:PSR
author: Irene Gargantini
title: Parallel Square-Root Iterations for Multiple Roots
journal: j-COMPUT-MATH-APPL
volume: 6
number: 3
pages: 279--288
year: 1980
CODEN: CMAPDK
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Wed Mar 1 18:51:19 MST 2017
bibtimestamp: 2017.03.01 18:51:19 MST
URL: http://www.sciencedirect.com/science/article/pii/0898122180900358
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-jr
journalURL: http://www.sciencedirect.com/science/journal/08981221/
rawauthor: Irene Gargantini
rawtitle: Parallel Square-Root Iterations for Multiple Roots
bibsource:
https://www.math.utah.edu/pub/tex/bib/computmathappl1980.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Gargantini:1980:PSR,
  author =       "Irene Gargantini",
  title =        "Parallel Square-Root Iterations for Multiple Roots",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "6",
  number =       "3",
  pages =        "279--288",
  month =        "????",
  year =         "1980",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 18:51:19 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0898122180900358",
  acknowledgement = ack-jr # " and " # ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221/",
}


bibtype: unpublished
filename: elefunt.bib
label: Kahan:1980:SPI
author: W. Kahan
title: Software $ sqrt x $ for the Proposed IEEE Floating-Point Standard
institution: inst-BERKELEY-CS
address: inst-BERKELEY-CS:adr
day: 25
month: aug
monthnumber: 8
year: 1980
bibdate: Mon Apr 25 18:24:02 2005
bibtimestamp: 2005.04.25 18:24:02 ???
note: Manuscript
acknowledgement: ack-nhfb
rawauthor: W. Kahan
rawnote: Manuscript
rawtitle: Software $ \sqrt x $ for the Proposed {IEEE Floating-Point Standard}
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Unpublished{Kahan:1980:SPI,
  author =       "W. Kahan",
  title =        "Software $ \sqrt x $ for the Proposed {IEEE
                 Floating-Point Standard}",
  institution =  inst-BERKELEY-CS,
  address =      inst-BERKELEY-CS:adr,
  pages =        "????",
  day =          "25",
  month =        aug,
  year =         "1980",
  bibdate =      "Mon Apr 25 18:24:02 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Manuscript",
  acknowledgement = ack-nhfb,
  mynote =       "Dated August 25 1980",
}


bibtype: article
filename: elefunt.bib
label: Kasperkovitz:1980:AAM
author: P. Kasperkovitz
title: Asymptotic approximations for modified Bessel functions
journal: j-J-MATH-PHYS
volume: 21
number: 1
pages: 6--13
month: jan
monthnumber: 1
year: 1980
CODEN: JMAPAQ
DOI: https://doi.org/10.1063/1.524310
ISSNL: 0022-2488 OR 00222488
MRclass: 33A40
MRnumber: 81a:33012
MRreviewer: N. Hayek Calil
bibdate: Sat Oct 29 18:18:22 MDT 2011
bibtimestamp: 2011.10.29 18:18:22 MDT
URL: http://jmp.aip.org/resource/1/jmapaq/v21/i1/p6_s1
fjournal: Journal of Mathematical Physics
acknowledgement: ack-nhfb
journalURL: http://jmp.aip.org/
onlinedate: 21 July 2008
rawauthor: P. Kasperkovitz
rawtitle: Asymptotic approximations for modified {Bessel} functions
bibsource:
http://jmp.aip.org/; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jmathphys1980.bib

entry:
@Article{Kasperkovitz:1980:AAM,
  author =       "P. Kasperkovitz",
  title =        "Asymptotic approximations for modified {Bessel}
                 functions",
  journal =      j-J-MATH-PHYS,
  volume =       "21",
  number =       "1",
  pages =        "6--13",
  month =        jan,
  year =         "1980",
  CODEN =        "JMAPAQ",
  DOI =          "https://doi.org/10.1063/1.524310",
  ISSN =         "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
  ISSN-L =       "0022-2488",
  MRclass =      "33A40",
  MRnumber =     "81a:33012",
  MRreviewer =   "N. Hayek Calil",
  bibdate =      "Sat Oct 29 18:18:22 MDT 2011",
  bibsource =    "http://jmp.aip.org/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jmathphys1980.bib",
  URL =          "http://jmp.aip.org/resource/1/jmapaq/v21/i1/p6_s1",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Physics",
  journal-URL =  "http://jmp.aip.org/",
  onlinedate =   "21 July 2008",
  pagecount =    "8",
}


bibtype: article
filename: elefunt.bib
label: Langebartel:1980:FER
author: R. G. Langebartel
title: Fourier expansions of rational fractions of elliptic integrals and Jacobian elliptic functions
journal: j-SIAM-J-MATH-ANA
volume: 11
number: 3
pages: 506--513
month: may
monthnumber: 5
year: 1980
CODEN: SJMAAH
ISSN: 0036-1410 (print), 1095-7154 (electronic) OR 00361410 (print), 10957154 (electronic)
ISSNL: 0036-1410 OR 00361410
MRclass: 42A16 (33A25)
MRnumber: 81e:42008
MRreviewer: R. C. Varma
bibdate: Sat Dec 5 18:14:13 MST 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1998.12.05 18:14:13 MST
fjournal: SIAM Journal on Mathematical Analysis
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sima
rawauthor: R. G. Langebartel
rawtitle: {Fourier} expansions of rational fractions of elliptic integrals and {Jacobian} elliptic functions
entry:
@Article{Langebartel:1980:FER,
  author =       "R. G. Langebartel",
  title =        "{Fourier} expansions of rational fractions of elliptic
                 integrals and {Jacobian} elliptic functions",
  journal =      j-SIAM-J-MATH-ANA,
  volume =       "11",
  number =       "3",
  pages =        "506--513",
  month =        may,
  year =         "1980",
  CODEN =        "SJMAAH",
  ISSN =         "0036-1410 (print), 1095-7154 (electronic)",
  ISSN-L =       "0036-1410",
  MRclass =      "42A16 (33A25)",
  MRnumber =     "81e:42008",
  MRreviewer =   "R. C. Varma",
  bibdate =      "Sat Dec 5 18:14:13 MST 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Mathematical Analysis",
  journal-URL =  "http://epubs.siam.org/sima",
}


bibtype: inproceedings
filename: elefunt.bib
label: Maksymiv:1980:APT
author: E. M. Maksymiv
booktitle: Differentsialnye Uravneniya i ikh Prilozhen
title: Approximate properties of Thiele's formula in a class of elementary functions. (Russian)
volume: 141
publisher: Vestnik L'vov. Politekhn. Inst.
address: L'vov, USSR
pages: 55--56
year: 1980
MRclass: 119.65D20
MRnumber: 81i:65021
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
language: Russian
acknowledgement: ack-nhfb
rawauthor: E. M. Maksymiv
rawbooktitle: Differentsialnye Uravneniya i ikh Prilozhen
rawtitle: Approximate properties of {Thiele}'s formula in a class of elementary functions. ({Russian})
entry:
@InProceedings{Maksymiv:1980:APT,
  author =       "E. M. Maksymiv",
  booktitle =    "Differentsialnye Uravneniya i ikh Prilozhen",
  title =        "Approximate properties of {Thiele}'s formula in a
                 class of elementary functions. ({Russian})",
  volume =       "141",
  publisher =    "Vestnik L'vov. Politekhn. Inst.",
  address =      "L'vov, USSR",
  pages =        "55--56",
  year =         "1980",
  MRclass =      "119.65D20",
  MRnumber =     "81i:65021",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  language =     "Russian",
}


bibtype: article
filename: elefunt.bib
label: Moran:1980:CND
author: P. A. P. Moran
title: Calculation of the Normal Distribution Function
journal: j-BIOMETRIKA
volume: 67
number: 3
pages: 675--676
month: dec
monthnumber: 12
year: 1980
CODEN: BIOKAX
DOI: https://doi.org/10.1093/biomet/67.3.675; https://doi.org/10.2307/2335138
ISSN: 0006-3444 (print), 1464-3510 (electronic) OR 00063444 (print), 14643510 (electronic)
ISSNL: 0006-3444 OR 00063444
MRclass: 62E30
MRnumber: 601106 (82d:62044)
MRreviewer: G. P. Bhattacharjee
bibdate: Sat Jun 21 14:34:26 MDT 2014
bibtimestamp: 2014.06.21 14:34:26 MDT
URL: http://www.jstor.org/stable/2335138
fjournal: Biometrika
acknowledgement: ack-nhfb
journalURL: http://biomet.oxfordjournals.org/content/by/year; http://www.jstor.org/journals/00063444.html
rawauthor: P. A. P. Moran
rawtitle: Calculation of the Normal Distribution Function
bibsource:
http://www.jstor.org/journals/00063444.html; http://www.jstor.org/stable/i315495; https://www.math.utah.edu/pub/tex/bib/biometrika1980.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Moran:1980:CND,
  author =       "P. A. P. Moran",
  title =        "Calculation of the Normal Distribution Function",
  journal =      j-BIOMETRIKA,
  volume =       "67",
  number =       "3",
  pages =        "675--676",
  month =        dec,
  year =         "1980",
  CODEN =        "BIOKAX",
  DOI =          "https://doi.org/10.1093/biomet/67.3.675;
                 https://doi.org/10.2307/2335138",
  ISSN =         "0006-3444 (print), 1464-3510 (electronic)",
  ISSN-L =       "0006-3444",
  MRclass =      "62E30",
  MRnumber =     "601106 (82d:62044)",
  MRreviewer =   "G. P. Bhattacharjee",
  bibdate =      "Sat Jun 21 14:34:26 MDT 2014",
  bibsource =    "http://www.jstor.org/journals/00063444.html;
                 http://www.jstor.org/stable/i315495;
                 https://www.math.utah.edu/pub/tex/bib/biometrika1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.jstor.org/stable/2335138",
  acknowledgement = ack-nhfb,
  fjournal =     "Biometrika",
  journal-URL =  "http://biomet.oxfordjournals.org/content/by/year;
                 http://www.jstor.org/journals/00063444.html",
}


bibtype: article
filename: elefunt.bib
label: OBrien:1980:SBF
author: D. M. O'Brien
title: Spherical Bessel functions of large order
journal: j-J-COMPUT-PHYS
volume: 36
number: 1
pages: 128--132
month: jun
monthnumber: 6
year: 1980
CODEN: JCTPAH
DOI: https://doi.org/10.1016/0021-9991(80)90177-1
ISSN: 0021-9991 (print), 1090-2716 (electronic) OR 00219991 (print), 10902716 (electronic)
ISSNL: 0021-9991 OR 00219991
bibdate: Sun Jan 1 15:59:01 MST 2012
bibtimestamp: 2012.01.01 15:59:01 MST
URL: http://www.sciencedirect.com/science/article/pii/0021999180901771
fjournal: Journal of Computational Physics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00219991/
rawauthor: D. M. O'Brien
rawtitle: Spherical {Bessel} functions of large order
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jcomputphys1980.bib

abstract:
This note introduces functions $ b_n(x) $, related to spherical Bessel functions $ j_n(x) $ and $ y_n(x) $. They are scaled so that they are bounded functions of $n$ and polynomially bounded functions of $x$, and therefore avoid the problems of underflow and overflow which are so common with Bessel functions. They can be generated from a stable recurrence relation for which starting values are readily computable.

rawabstract:
This note introduces functions $ b_n(x) $, related to spherical Bessel functions $ j_n(x) $ and $ y_n(x) $. They are scaled so that they are bounded functions of $n$ and polynomially bounded functions of $x$, and therefore avoid the problems of underflow and overflow which are so common with Bessel functions. They can be generated from a stable recurrence relation for which starting values are readily computable.

entry:
@Article{OBrien:1980:SBF,
  author =       "D. M. O'Brien",
  title =        "Spherical {Bessel} functions of large order",
  journal =      j-J-COMPUT-PHYS,
  volume =       "36",
  number =       "1",
  pages =        "128--132",
  month =        jun,
  year =         "1980",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(80)90177-1",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Sun Jan 1 15:59:01 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1980.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0021999180901771",
  abstract =     "This note introduces functions $ b_n(x) $, related to
                 spherical Bessel functions $ j_n(x) $ and $ y_n(x) $.
                 They are scaled so that they are bounded functions of
                 $n$ and polynomially bounded functions of $x$, and
                 therefore avoid the problems of underflow and overflow
                 which are so common with Bessel functions. They can be
                 generated from a stable recurrence relation for which
                 starting values are readily computable.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}


bibtype: inproceedings
filename: elefunt.bib
label: Olver:1980:UAG
author: F. W. J. Olver
title: Unrestricted algorithms for generating elementary functions
crossref: Alefeld:1980:PSE
pages: 131--140
year: 1980
MRclass: 65G05 (65D15)
MRnumber: 82b:65034
MRreviewer: John Todd
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
acknowledgement: ack-nhfb
rawauthor: F. W. J. Olver
rawtitle: Unrestricted algorithms for generating elementary functions
entry:
@InProceedings{Olver:1980:UAG,
  author =       "F. W. J. Olver",
  title =        "Unrestricted algorithms for generating elementary
                 functions",
  crossref =     "Alefeld:1980:PSE",
  pages =        "131--140",
  year =         "1980",
  MRclass =      "65G05 (65D15)",
  MRnumber =     "82b:65034",
  MRreviewer =   "John Todd",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Pedersen:1980:HBM
author: P. W. Pedersen
title: Hvordan beregner man kvadratroden? toenglish How do you calculate the square root? endtoenglish
journal: Elektronik (Denmark)
number: 4
pages: 18--21
month: apr
monthnumber: 4
year: 1980
bibdate: Fri Sep 16 16:30:41 1994
bibtimestamp: 1994.09.16 16:30:41 ???
acknowledgement: ack-nj
rawauthor: P. W. Pedersen
rawtitle: Hvordan beregner man kvadratroden? \toenglish {How do you calculate the square root?} \endtoenglish
entry:
@Article{Pedersen:1980:HBM,
  author =       "P. W. Pedersen",
  title =        "Hvordan beregner man kvadratroden? \toenglish {How do
                 you calculate the square root?} \endtoenglish",
  journal =      "Elektronik (Denmark)",
  volume =       "??",
  number =       "4",
  pages =        "18--21",
  month =        apr,
  year =         "1980",
  bibdate =      "Fri Sep 16 16:30:41 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: book
filename: elefunt.bib
label: Popov:1980:PFD
author: B. A. Popov and G. S. Tesler
publisher: Naukova Dumka
address: Kiev, USSR
pages: 351
year: 1980
MRclass: 65D15 (41-02 65D07)
MRnumber: 602955
bibdate: Tue Jan 24 08:23:12 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.01.24 08:23:12 ???
note: Nauka i tekhnicheskii progress. [Science and technical progress]
acknowledgement: ack-nhfb
rawauthor: B. A. Popov and G. S. Tesler
rawnote: Nauka i tekhnicheskii progress. [Science and technical progress]
title:
Priblizhenie funktsii dlya tekhnicheskikh prilozhenii. (Russian) [Approximation of functions for technical applications]

rawtitle:
Priblizhenie funktsii dlya tekhnicheskikh prilozhenii. ({Russian}) [{Approximation} of functions for technical applications]

entry:
@Book{Popov:1980:PFD,
  author =       "B. A. Popov and G. S. Tesler",
  title =        "Priblizhenie funktsii dlya tekhnicheskikh prilozhenii.
                 ({Russian}) [{Approximation} of functions for technical
                 applications]",
  publisher =    "Naukova Dumka",
  address =      "Kiev, USSR",
  pages =        "351",
  year =         "1980",
  MRclass =      "65D15 (41-02 65D07)",
  MRnumber =     "602955",
  bibdate =      "Tue Jan 24 08:23:12 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Nauka i tekhnicheskii progress. [Science and technical
                 progress]",
  acknowledgement = ack-nhfb # " and " # ack-mv,
}


bibtype: article
filename: elefunt.bib
label: Rengarajan:1980:MFI
author: S. R. Rengarajan and J. E. Lewis
title: Mathieu Functions of Integral Order and Real Arguments
journal: j-IEEE-TRANS-MICROWAVE-THEORY-TECH
volume: 28
number: 3
pages: 276--277
month: mar
monthnumber: 3
year: 1980
CODEN: IETMAB
DOI: https://doi.org/10.1109/TMTT.1980.1130060
ISSN: 0018-9480 (print), 1557-9670 (electronic) OR 00189480 (print), 15579670 (electronic)
ISSNL: 0018-9480 OR 00189480
bibdate: Sat Oct 30 10:09:01 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.30 10:09:01 ???
fjournal: IEEE transactions on microwave theory and techniques
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=22
rawauthor: S. R. Rengarajan and J. E. Lewis
rawtitle: {Mathieu} Functions of Integral Order and Real Arguments
abstract:
To compute Mathieu functions, modified Mathieu functions and related parameters for integral orders and real arguments, encountered in wave propagation involving elliptic geometries.

remark:
Fullerton: A long FORTRAN program is very briefly described. This work is superior to that of Clemm (1969), because $q$ may be negative.

rawabstract:
To compute Mathieu functions, modified Mathieu functions and related parameters for integral orders and real arguments, encountered in wave propagation involving elliptic geometries.

entry:
@Article{Rengarajan:1980:MFI,
  author =       "S. R. Rengarajan and J. E. Lewis",
  title =        "{Mathieu} Functions of Integral Order and Real
                 Arguments",
  journal =      j-IEEE-TRANS-MICROWAVE-THEORY-TECH,
  volume =       "28",
  number =       "3",
  pages =        "276--277",
  month =        mar,
  year =         "1980",
  CODEN =        "IETMAB",
  DOI =          "https://doi.org/10.1109/TMTT.1980.1130060",
  ISSN =         "0018-9480 (print), 1557-9670 (electronic)",
  ISSN-L =       "0018-9480",
  bibdate =      "Sat Oct 30 10:09:01 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "To compute Mathieu functions, modified Mathieu
                 functions and related parameters for integral orders
                 and real arguments, encountered in wave propagation
                 involving elliptic geometries.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "IEEE transactions on microwave theory and techniques",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=22",
  remark =       "Fullerton: A long FORTRAN program is very briefly
                 described. This work is superior to that of Clemm
                 (1969), because $q$ may be negative.",
}


bibtype: article
filename: elefunt.bib
label: Schell:1980:AEU
author: Hans-Joachim Schell
journal: Wissenschaftliche Zeitschrift der Technischen Hochschule Karl-Marx-Stadt
volume: 22
number: 5
pages: 477 485
year: 1980
bibdate: Sat Feb 18 15:11:46 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.02.18 15:11:46 ???
keywords: incomplete gamma function; uniform asymptotic expansions
language: German
acknowledgement: ack-nhfb
ajournal: Wiss. Schr. Tech. Univ. Karl-Marx-Stadt
rawauthor: Hans-Joachim Schell
title:
Asymptotische Entwicklungen fur die unvollstandige Gammafunktion. (German) [Asymptotic developments for the incomplete gamma function]

rawtitle:
{Asymptotische Entwicklungen f{\"u}r die unvollst{\"a}ndige Gammafunktion}. ({German}) [{Asymptotic} developments for the incomplete gamma function]

entry:
@Article{Schell:1980:AEU,
  author =       "Hans-Joachim Schell",
  title =        "{Asymptotische Entwicklungen f{\"u}r die
                 unvollst{\"a}ndige Gammafunktion}. ({German})
                 [{Asymptotic} developments for the incomplete gamma
                 function]",
  journal =      "{Wissenschaftliche Zeitschrift der Technischen
                 Hochschule Karl-Marx-Stadt}",
  volume =       "22",
  number =       "5",
  pages =        "477 485",
  month =        "????",
  year =         "1980",
  bibdate =      "Sat Feb 18 15:11:46 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "{Wiss. Schr. Tech. Univ. Karl-Marx-Stadt}",
  keywords =     "incomplete gamma function; uniform asymptotic
                 expansions",
  language =     "German",
}


bibtype: article
filename: elefunt.bib
label: Schonfelder:1980:VHA
author: J. L. Schonfelder
title: Very high accuracy Chebyshev expansions for the basic trigonometric functions
journal: j-MATH-COMPUT
volume: 34
number: 149
pages: 237--244
month: jan
monthnumber: 1
year: 1980
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 65D20
MRnumber: 81f:65016
MRreviewer: Claude Carasso
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
remark: Fullerton: 40D coefficients for the sine, cosine and tangent are given.
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: J. L. Schonfelder
rawtitle: Very high accuracy {Chebyshev} expansions for the basic trigonometric functions
entry:
@Article{Schonfelder:1980:VHA,
  author =       "J. L. Schonfelder",
  title =        "Very high accuracy {Chebyshev} expansions for the
                 basic trigonometric functions",
  journal =      j-MATH-COMPUT,
  volume =       "34",
  number =       "149",
  pages =        "237--244",
  month =        jan,
  year =         "1980",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65D20",
  MRnumber =     "81f:65016",
  MRreviewer =   "Claude Carasso",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  remark =       "Fullerton: 40D coefficients for the sine, cosine and
                 tangent are given.",
}


bibtype: book
filename: elefunt.bib
label: Sneddon:1980:SFM
author: Ian Naismith Sneddon
title: Special Functions of Mathematical Physics and Chemistry
publisher: Longman
address: London, UK
edition: Third
pages: ix + 182
year: 1980
ISBN: 0-582-44396-2 (paperback) OR 0582443962 (paperback)
ISBN13: 978-0-582-44396-9 (paperback) OR 9780582443969 (paperback)
LCCN: QA351 .S64 1980
bibdate: Sat Oct 30 18:25:01 MDT 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2010.10.30 18:25:01 MDT
series: Longman mathematical texts
remark: See first edition cite Sneddon:1956:SFM and second edition cite Sneddon:1961:SFM.
subject: Functions, Special
acknowledgement: ack-nhfb
rawauthor: Ian Naismith Sneddon
rawtitle: Special Functions of Mathematical Physics and Chemistry
entry:
@Book{Sneddon:1980:SFM,
  author =       "Ian Naismith Sneddon",
  title =        "Special Functions of Mathematical Physics and
                 Chemistry",
  publisher =    "Longman",
  address =      "London, UK",
  edition =      "Third",
  pages =        "ix + 182",
  year =         "1980",
  ISBN =         "0-582-44396-2 (paperback)",
  ISBN-13 =      "978-0-582-44396-9 (paperback)",
  LCCN =         "QA351 .S64 1980",
  bibdate =      "Sat Oct 30 18:25:01 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Longman mathematical texts",
  acknowledgement = ack-nhfb,
  remark =       "See first edition \cite{Sneddon:1956:SFM} and second
                 edition \cite{Sneddon:1961:SFM}.",
  subject =      "Functions, Special",
}


bibtype: incollection
filename: elefunt.bib
label: Tretjakov:1980:PSE
author: V. A. Tret'jakov
booktitle: Mathematical analysis and the theory of functions (Russian)
publisher: Moskov. Oblast. Ped. Inst.
address: Moscow, USSR
pages: 99--106
year: 1980
MRclass: 30G35 (78A35)
MRnumber: 82i:30069
MRreviewer: Toma V. Tonev
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
language: Russian
acknowledgement: ack-nhfb
rawauthor: V. A. Tret'jakov
rawbooktitle: Mathematical analysis and the theory of functions ({Russian})
title:
On the properties of some elementary functions that are defined on the algebra of bicomplex numbers. (Russian)

rawtitle:
On the properties of some elementary functions that are defined on the algebra of bicomplex numbers. ({Russian})

entry:
@InCollection{Tretjakov:1980:PSE,
  author =       "V. A. Tret'jakov",
  booktitle =    "Mathematical analysis and the theory of functions
                 ({Russian})",
  title =        "On the properties of some elementary functions that
                 are defined on the algebra of bicomplex numbers.
                 ({Russian})",
  publisher =    "Moskov. Oblast. Ped. Inst.",
  address =      "Moscow, USSR",
  pages =        "99--106",
  year =         "1980",
  MRclass =      "30G35 (78A35)",
  MRnumber =     "82i:30069",
  MRreviewer =   "Toma V. Tonev",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  language =     "Russian",
}


bibtype: article
filename: elefunt.bib
label: Tretter:1980:ASA
author: Marietta J. Tretter and G. W. Walster
title: Analytic subtraction applied to the incomplete gamma and beta functions
journal: j-SIAM-J-SCI-STAT-COMP
volume: 1
number: 3
pages: 321--326
month: sep
monthnumber: 9
year: 1980
CODEN: SIJCD4
DOI: https://doi.org/10.1137/0901022
ISSN: 0196-5204 OR 01965204
ISSNL: 0196-5204 OR 01965204
MRclass: 65D20 (33A15)
MRnumber: 81m:65029
MRreviewer: Anton Hut'a
bibdate: Mon Mar 31 09:58:49 MDT 2014
bibtimestamp: 2014.03.31 09:58:49 MDT
fjournal: SIAM Journal on Scientific and Statistical Computing
keywords: analytic subtraction; continued fraction; incomplete beta function; incomplete gamma function
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/loi/sjoce3
onlinedate: September 1980
rawauthor: Marietta J. Tretter and G. W. Walster
rawtitle: Analytic subtraction applied to the incomplete gamma and beta functions
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/siamjscistatcomp.bib

entry:
@Article{Tretter:1980:ASA,
  author =       "Marietta J. Tretter and G. W. Walster",
  title =        "Analytic subtraction applied to the incomplete gamma
                 and beta functions",
  journal =      j-SIAM-J-SCI-STAT-COMP,
  volume =       "1",
  number =       "3",
  pages =        "321--326",
  month =        sep,
  year =         "1980",
  CODEN =        "SIJCD4",
  DOI =          "https://doi.org/10.1137/0901022",
  ISSN =         "0196-5204",
  ISSN-L =       "0196-5204",
  MRclass =      "65D20 (33A15)",
  MRnumber =     "81m:65029",
  MRreviewer =   "Anton Hut'a",
  bibdate =      "Mon Mar 31 09:58:49 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjscistatcomp.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific and Statistical Computing",
  journal-URL =  "http://epubs.siam.org/loi/sjoce3",
  keywords =     "analytic subtraction; continued fraction; incomplete
                 beta function; incomplete gamma function",
  onlinedate =   "September 1980",
}


bibtype: phdthesis
filename: elefunt.bib
label: vonGudenberg:1980:EAR
author: J. Wolff von Gudenberg
type: Dissertation
school: Universitat Karlsruhe
address: Karlsruhe, Germany
year: 1980
bibdate: Sun Oct 25 10:29:29 1998
bibsource: garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1998.10.25 10:29:29 ???
acknowledgement: ack-nj
rawauthor: J. Wolff {von Gudenberg}
title:
Einbettung allgemeiner Rechnerarithmetik in Pascal mittels eines Operatorkonzepts und Implementierung der Standardfunktionen mit optimaler Genauigkeit toenglish Embedding a General Computer Arithmetic in Pascal by Means of an Operator Concept and the Implementation of Elementary Functions with Optimal Accuracy endtoenglish 

rawtitle:
{Einbettung allgemeiner Rechnerarithmetik in Pascal mittels eines Operatorkonzepts und Implementierung der Standardfunktionen mit optimaler Genauigkeit} \toenglish {Embedding a General Computer Arithmetic in Pascal by Means of an Operator Concept and the Implementation of Elementary Functions with Optimal Accuracy} \endtoenglish

entry:
@PhdThesis{vonGudenberg:1980:EAR,
  author =       "J. Wolff {von Gudenberg}",
  title =        "{Einbettung allgemeiner Rechnerarithmetik in Pascal
                 mittels eines Operatorkonzepts und Implementierung der
                 Standardfunktionen mit optimaler Genauigkeit}
                 \toenglish {Embedding a General Computer Arithmetic in
                 Pascal by Means of an Operator Concept and the
                 Implementation of Elementary Functions with Optimal
                 Accuracy} \endtoenglish",
  type =         "Dissertation",
  school =       "Universit{\"a}t Karlsruhe",
  address =      "Karlsruhe, Germany",
  pages =        "????",
  year =         "1980",
  bibdate =      "Sun Oct 25 10:29:29 1998",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nj,
}


bibtype: article
filename: elefunt.bib
label: Waldecker:1980:NSR
author: D. E. Waldecker
title: Nonrestoring Square Root with Simplified Answer Generation
journal: j-IBM-TDB
volume: 22
number: 11
pages: 4807--4808
month: apr
monthnumber: 4
year: 1980
CODEN: IBMTAA
ISSN: 0018-8689 OR 00188689
bibdate: Thu Sep 1 10:15:41 1994
bibtimestamp: 1994.09.01 10:15:41 ???
fjournal: IBM Technical Disclosure Bulletin
acknowledgement: ack-nj
rawauthor: D. E. Waldecker
rawtitle: Nonrestoring Square Root with Simplified Answer Generation
entry:
@Article{Waldecker:1980:NSR,
  author =       "D. E. Waldecker",
  title =        "Nonrestoring Square Root with Simplified Answer
                 Generation",
  journal =      j-IBM-TDB,
  volume =       "22",
  number =       "11",
  pages =        "4807--4808",
  month =        apr,
  year =         "1980",
  CODEN =        "IBMTAA",
  ISSN =         "0018-8689",
  bibdate =      "Thu Sep 1 10:15:41 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "IBM Technical Disclosure Bulletin",
}


bibtype: article
filename: elefunt.bib
label: Andrews:1981:EFM
author: M. Andrews and D. Jaeger and S. F. McCormick and G. D. Taylor
title: Evaluation of Functions on Microcomputers: $ exp (x) $
journal: j-COMPUT-MATH-APPL
volume: 7
number: 6
pages: 503--508
year: 1981
CODEN: CMAPDK
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Wed Mar 1 18:51:21 MST 2017
bibtimestamp: 2017.03.01 18:51:21 MST
URL: http://www.sciencedirect.com/science/article/pii/0898122181900341
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-nj
journalURL: http://www.sciencedirect.com/science/journal/08981221/
rawauthor: M. Andrews and D. Jaeger and S. F. McCormick and G. D. Taylor
rawtitle: Evaluation of Functions on Microcomputers: $ \exp (x) $
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/computmathappl1980.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Andrews:1981:EFM,
  author =       "M. Andrews and D. Jaeger and S. F. McCormick and G. D.
                 Taylor",
  title =        "Evaluation of Functions on Microcomputers: $ \exp (x)
                 $",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "7",
  number =       "6",
  pages =        "503--508",
  month =        "????",
  year =         "1981",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 18:51:21 MST 2017",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/computmathappl1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0898122181900341",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221/",
  xxmonth =      "(none)",
}


bibtype: article
filename: elefunt.bib
label: Arscott:1981:LBB
author: F. M. Arscott
title: The land beyond Bessel: a survey of higher special functions
journal: j-LECT-NOTES-MATH
volume: 846
pages: 26--45
year: 1981
CODEN: LNMAA2
DOI: https://doi.org/10.1007/BFb0089822
ISBN: 3-540-10569-7 (print), 3-540-38538-X (e-book) OR 3540105697 (print), 354038538X (ebook)
ISSN: 0075-8434 (print), 1617-9692 (electronic) OR 00758434 (print), 16179692 (electronic)
ISSNL: 0075-8434 OR 00758434
bibdate: Fri May 9 19:07:31 MDT 2014
bibtimestamp: 2014.05.09 19:07:31 MDT
URL: http://link.springer.com/chapter/10.1007/BFb0089822/
fjournal: Lecture Notes in Mathematics
acknowledgement: ack-nhfb
bookDOI: https://doi.org/10.1007/BFb0089819
bookURL: http://www.springerlink.com/content/978-3-540-38538-7
journalURL: http://link.springer.com/bookseries/304
rawauthor: F. M. Arscott
rawtitle: The land beyond {Bessel}: a survey of higher special functions
ISBN13:
978-3-540-10569-5 (print), 978-3-540-38538-7 (e-book) OR 9783540105695 (print), 9783540385387 (ebook)

bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/lnm1980.bib

entry:
@Article{Arscott:1981:LBB,
  author =       "F. M. Arscott",
  title =        "The land beyond {Bessel}: a survey of higher special
                 functions",
  journal =      j-LECT-NOTES-MATH,
  volume =       "846",
  pages =        "26--45",
  year =         "1981",
  CODEN =        "LNMAA2",
  DOI =          "https://doi.org/10.1007/BFb0089822",
  ISBN =         "3-540-10569-7 (print), 3-540-38538-X (e-book)",
  ISBN-13 =      "978-3-540-10569-5 (print), 978-3-540-38538-7
                 (e-book)",
  ISSN =         "0075-8434 (print), 1617-9692 (electronic)",
  ISSN-L =       "0075-8434",
  bibdate =      "Fri May 9 19:07:31 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/lnm1980.bib",
  URL =          "http://link.springer.com/chapter/10.1007/BFb0089822/",
  acknowledgement = ack-nhfb,
  book-DOI =     "https://doi.org/10.1007/BFb0089819",
  book-URL =     "http://www.springerlink.com/content/978-3-540-38538-7",
  fjournal =     "Lecture Notes in Mathematics",
  journal-URL =  "http://link.springer.com/bookseries/304",
}


bibtype: article
filename: elefunt.bib
label: Banuelos:1981:PCF
author: Alicia Banuelos and Ricardo Angel Depine and Roberto Claudio Mancini
title: A program for computing the Fermi--Dirac functions
journal: j-COMP-PHYS-COMM
volume: 21
number: 3
pages: 315--322
month: jan
monthnumber: 1
year: 1981
CODEN: CPHCBZ
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Wed Feb 5 09:02:18 MST 2014
bibtimestamp: 2014.02.05 09:02:18 MST
URL: http://www.sciencedirect.com/science/article/pii/0010465581900126
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655/
rawauthor: Alicia Ba{\~n}uelos and Ricardo Angel Depine and Roberto Claudio Mancini
rawtitle: A program for computing the {Fermi--Dirac} functions
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/d/dirac-p-a-m.bib; https://www.math.utah.edu/pub/bibnet/authors/f/fermi-enrico.bib; https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Banuelos:1981:PCF,
  author =       "Alicia Ba{\~n}uelos and Ricardo Angel Depine and
                 Roberto Claudio Mancini",
  title =        "A program for computing the {Fermi--Dirac} functions",
  journal =      j-COMP-PHYS-COMM,
  volume =       "21",
  number =       "3",
  pages =        "315--322",
  month =        jan,
  year =         "1981",
  CODEN =        "CPHCBZ",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Wed Feb 5 09:02:18 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/d/dirac-p-a-m.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/f/fermi-enrico.bib;
                 https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0010465581900126",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655/",
}


bibtype: article
filename: elefunt.bib
label: Baratella:1981:ABF
author: P. Baratella and M. Garetto and G. Vinardi
title: Approximation of the Bessel function $ J_nu (x) $ by numerical integration
journal: j-J-COMPUT-APPL-MATH
volume: 7
number: 2
pages: 87--91
month: jun
monthnumber: 6
year: 1981
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 11:59:21 MST 2017
bibtimestamp: 2017.02.25 11:59:21 MST
URL: http://www.sciencedirect.com/science/article/pii/0771050X81900401
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: P. Baratella and M. Garetto and G. Vinardi
rawtitle: Approximation of the {Bessel} function {$ J_\nu (x) $} by numerical integration
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1980.bib

entry:
@Article{Baratella:1981:ABF,
  author =       "P. Baratella and M. Garetto and G. Vinardi",
  title =        "Approximation of the {Bessel} function {$ J_\nu (x) $}
                 by numerical integration",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "7",
  number =       "2",
  pages =        "87--91",
  month =        jun,
  year =         "1981",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 11:59:21 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1980.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0771050X81900401",
  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: Barnett:1981:ARI
author: A. R. Barnett
journal: j-COMP-PHYS-COMM
volume: 21
number: 3
pages: 297--314
month: jan
monthnumber: 1
year: 1981
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/0010-4655(81)90011-4
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Thu Apr 24 10:35:27 2008
bibtimestamp: 2008.04.24 10:35:27 ???
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: A. R. Barnett
title:
An algorithm for regular and irregular Coulomb and Bessel functions of real order to machine accuracy

bibsource:
https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

abstract:
We describe an algorithm to evaluate a wide class of functions and their derivatives, to extreme precision (25--30S) if required, which does not use any function calls other than square root. The functions are the Coulomb functions of positive argument ($ F_lambda (x, eta ) $, $ G_lambda (x, eta ) $, $ x > 0 $, $ eta $, $ lambda $ real) and hence, as special cases with $ eta = 0 $, the cylindrical Bessel functions ($ J_mu (x) $, $ Y_mu (x) $, $ x > 0 $, $ mu $ real), the spherical Bessel functions ($ i_lambda (x) $, $ y_lambda (x) $, $ x > 0 $, $ lambda $ real), Airy functions of negative argument $ textrm Ai( - x) $, $ textrm Bi( - x) $ and others. The present method has a number of attractive features: both the regular and irregular solution are calculated, all others of the functions can be produced from a specified minimum (not necessarily zero) to a specified maximum, functions of a single order can be found without all of the orders from zero, the derivatives of the functions arise naturally in the solution and are readily available, the results are available to different precisions from the same subroutine (in contrast to rational approximation techniques) and the methods can be used for estimating final accuracies. In addition, the sole constant required in the algorithm is $ pi $, no precalculated arrays of coefficients are needed, and the final accuracy is not dependent on that of other subroutines. The method works most efficiently in the region $ x approx 0.5 $ to $ x approx 1000 $ but outside this region the results are still reliable, even though the number of iterations within the subroutine rises. Even in these more asymptotic regions the unchanged algorithm can be used with known accuracy to test other specific subroutines more appropriate to these regions. The algorithm uses the recursion relations satisfied by the Coulomb functions and contains a significant advance over Miller's method for evaluating the ratio of successive minimal solutions ($ F_lambda + 1 / F_lambda $ ). It relies on the evaluation of two continued fractions and no infinite series is required for normalisation: instead the Wronskian is used.

rawabstract:
We describe an algorithm to evaluate a wide class of functions and their derivatives, to extreme precision (25--30S) if required, which does not use any function calls other than square root. The functions are the Coulomb functions of positive argument ($ F_\lambda (x, \eta) $, $ G_\lambda (x, \eta) $, $ x > 0 $, $ \eta $, $ \lambda $ real) and hence, as special cases with $ \eta = 0 $, the cylindrical Bessel functions ($ J_\mu (x) $, $ Y_\mu (x) $, $ x > 0 $, $ \mu $ real), the spherical Bessel functions ($ i_\lambda (x) $, $ y_\lambda (x) $, $ x > 0 $, $ \lambda $ real), Airy functions of negative argument $ \textrm {Ai}( - x) $, $ \textrm {Bi}( - x) $ and others. The present method has a number of attractive features: both the regular and irregular solution are calculated, all others of the functions can be produced from a specified minimum (not necessarily zero) to a specified maximum, functions of a single order can be found without all of the orders from zero, the derivatives of the functions arise naturally in the solution and are readily available, the results are available to different precisions from the same subroutine (in contrast to rational approximation techniques) and the methods can be used for estimating final accuracies. In addition, the sole constant required in the algorithm is $ \pi $, no precalculated arrays of coefficients are needed, and the final accuracy is not dependent on that of other subroutines. The method works most efficiently in the region $ x \approx 0.5 $ to $ x \approx 1000 $ but outside this region the results are still reliable, even though the number of iterations within the subroutine rises. Even in these more asymptotic regions the unchanged algorithm can be used with known accuracy to test other specific subroutines more appropriate to these regions. The algorithm uses the recursion relations satisfied by the Coulomb functions and contains a significant advance over Miller's method for evaluating the ratio of successive minimal solutions ($ F_\lambda + 1 / F_\lambda $ ). It relies on the evaluation of two continued fractions and no infinite series is required for normalisation: instead the Wronskian is used.

rawtitle:
An algorithm for regular and irregular {Coulomb} and {Bessel} functions of real order to machine accuracy

entry:
@Article{Barnett:1981:ARI,
  author =       "A. R. Barnett",
  title =        "An algorithm for regular and irregular {Coulomb} and
                 {Bessel} functions of real order to machine accuracy",
  journal =      j-COMP-PHYS-COMM,
  volume =       "21",
  number =       "3",
  pages =        "297--314",
  month =        jan,
  year =         "1981",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(81)90011-4",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Thu Apr 24 10:35:27 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "We describe an algorithm to evaluate a wide class of
                 functions and their derivatives, to extreme precision
                 (25--30S) if required, which does not use any function
                 calls other than square root. The functions are the
                 Coulomb functions of positive argument ($ F_\lambda (x,
                 \eta) $, $ G_\lambda (x, \eta) $, $ x > 0 $, $ \eta $,
                 $ \lambda $ real) and hence, as special cases with $
                 \eta = 0 $, the cylindrical Bessel functions ($ J_\mu
                 (x) $, $ Y_\mu (x) $, $ x > 0 $, $ \mu $ real), the
                 spherical Bessel functions ($ i_\lambda (x) $, $
                 y_\lambda (x) $, $ x > 0 $, $ \lambda $ real), Airy
                 functions of negative argument $ \textrm {Ai}( - x) $,
                 $ \textrm {Bi}( - x) $ and others. The present method
                 has a number of attractive features: both the regular
                 and irregular solution are calculated, all others of
                 the functions can be produced from a specified minimum
                 (not necessarily zero) to a specified maximum,
                 functions of a single order can be found without all of
                 the orders from zero, the derivatives of the functions
                 arise naturally in the solution and are readily
                 available, the results are available to different
                 precisions from the same subroutine (in contrast to
                 rational approximation techniques) and the methods can
                 be used for estimating final accuracies. In addition,
                 the sole constant required in the algorithm is $ \pi $,
                 no precalculated arrays of coefficients are needed, and
                 the final accuracy is not dependent on that of other
                 subroutines. The method works most efficiently in the
                 region $ x \approx 0.5 $ to $ x \approx 1000 $ but
                 outside this region the results are still reliable,
                 even though the number of iterations within the
                 subroutine rises. Even in these more asymptotic regions
                 the unchanged algorithm can be used with known accuracy
                 to test other specific subroutines more appropriate to
                 these regions. The algorithm uses the recursion
                 relations satisfied by the Coulomb functions and
                 contains a significant advance over Miller's method for
                 evaluating the ratio of successive minimal solutions ($
                 F_\lambda + 1 / F_\lambda $ ). It relies on the
                 evaluation of two continued fractions and no infinite
                 series is required for normalisation: instead the
                 Wronskian is used.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}


bibtype: article
filename: elefunt.bib
label: Bice:1981:AAS
author: P. K. Bice
title: Algorithm adds square root to micro's arithmetic capability
journal: j-ELECTRONIC-DESIGN
volume: 29
number: 11
pages: 146
month: may
monthnumber: 5
year: 1981
CODEN: ELODAW
ISSN: 0013-4872 (print), 1944-9550 (electronic) OR 00134872 (print), 19449550 (electronic)
ISSNL: 0013-4872 OR 00134872
bibdate: Thu Sep 1 10:15:42 1994
bibtimestamp: 1994.09.01 10:15:42 ???
fjournal: Electronic Design
acknowledgement: ack-nj
rawauthor: P. K. Bice
rawtitle: Algorithm adds square root to micro's arithmetic capability
entry:
@Article{Bice:1981:AAS,
  author =       "P. K. Bice",
  title =        "Algorithm adds square root to micro's arithmetic
                 capability",
  journal =      j-ELECTRONIC-DESIGN,
  volume =       "29",
  number =       "11",
  pages =        "146",
  month =        may,
  year =         "1981",
  CODEN =        "ELODAW",
  ISSN =         "0013-4872 (print), 1944-9550 (electronic)",
  ISSN-L =       "0013-4872",
  bibdate =      "Thu Sep 1 10:15:42 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Electronic Design",
}


bibtype: article
filename: elefunt.bib
label: Branrers:1981:RAZ
author: M. Branrers and R. Piessens and M. De Meue
title: Rational approximations for zeros of Bessel functions
journal: j-J-COMPUT-PHYS
volume: 42
number: 2
pages: 403--405
month: aug
monthnumber: 8
year: 1981
CODEN: JCTPAH
DOI: https://doi.org/10.1016/0021-9991(81)90253-9
ISSN: 0021-9991 (print), 1090-2716 (electronic) OR 00219991 (print), 10902716 (electronic)
ISSNL: 0021-9991 OR 00219991
bibdate: Sun Jan 1 15:59:07 MST 2012
bibtimestamp: 2012.01.01 15:59:07 MST
URL: http://www.sciencedirect.com/science/article/pii/0021999181902539
fjournal: Journal of Computational Physics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00219991/
rawauthor: M. Branrers and R. Piessens and M. {De Meue}
rawtitle: Rational approximations for zeros of {Bessel} functions
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jcomputphys1980.bib

entry:
@Article{Branrers:1981:RAZ,
  author =       "M. Branrers and R. Piessens and M. {De Meue}",
  title =        "Rational approximations for zeros of {Bessel}
                 functions",
  journal =      j-J-COMPUT-PHYS,
  volume =       "42",
  number =       "2",
  pages =        "403--405",
  month =        aug,
  year =         "1981",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(81)90253-9",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Sun Jan 1 15:59:07 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1980.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0021999181902539",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}


bibtype: article
filename: elefunt.bib
label: Campbell:1981:BFR
author: J. B. Campbell
title: Bessel functions $ I_nu (z) $ and $ K_nu (z) $ of real order and complex argument
journal: j-COMP-PHYS-COMM
volume: 24
number: 1
pages: 97--105
month: sep
monthnumber: 9
year: 1981
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/0010-4655(81)90109-0
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Mon Feb 13 10:27:59 MST 2012
bibtimestamp: 2012.02.13 10:27:59 MST
URL: http://www.sciencedirect.com/science/article/pii/0010465581901090
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: J. B. Campbell
rawtitle: {Bessel} functions {$ I_\nu (z) $} and {$ K_\nu (z) $} of real order and complex argument
bibsource:
https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Campbell:1981:BFR,
  author =       "J. B. Campbell",
  title =        "{Bessel} functions {$ I_\nu (z) $} and {$ K_\nu (z) $}
                 of real order and complex argument",
  journal =      j-COMP-PHYS-COMM,
  volume =       "24",
  number =       "1",
  pages =        "97--105",
  month =        sep # "\slash " # oct,
  year =         "1981",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(81)90109-0",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Feb 13 10:27:59 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0010465581901090",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}


bibtype: article
filename: elefunt.bib
label: Carlson:1981:AAI
author: B. C. Carlson and Elaine M. Notis
title: Algorithm 577: Algorithms for Incomplete Elliptic Integrals [S21]
journal: j-TOMS
volume: 7
number: 3
pages: 398--403
month: sep
monthnumber: 9
year: 1981
CODEN: ACMSCU
DOI: https://doi.org/10.1145/355958.355970
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Mon Aug 29 22:58:27 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.08.29 22:58:27 ???
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: B. C. Carlson and Elaine M. Notis
rawtitle: {Algorithm 577}: Algorithms for Incomplete Elliptic Integrals [{S21}]
keywords:
$R$-functions; elliptic integrals; inverse circular functions; inverse hyperbolic functions; logarithms

entry:
@Article{Carlson:1981:AAI,
  author =       "B. C. Carlson and Elaine M. Notis",
  title =        "{Algorithm 577}: Algorithms for Incomplete Elliptic
                 Integrals [{S21}]",
  journal =      j-TOMS,
  volume =       "7",
  number =       "3",
  pages =        "398--403",
  month =        sep,
  year =         "1981",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355958.355970",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 29 22:58:27 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "$R$-functions; elliptic integrals; inverse circular
                 functions; inverse hyperbolic functions; logarithms",
}


bibtype: article
filename: elefunt.bib
label: Chen:1981:AFD
author: Gang Chen
journal: Zhejiang Daxue Xuebao
volume: 3
pages: 141--149
year: 1981
MRclass: 26A09
MRnumber: 714 524
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
acknowledgement: ack-nhfb
rawauthor: Gang Chen
title:
An attempt to find the derivatives of elementary functions using the algorithmic language BCY. (Chinese)

rawtitle:
An attempt to find the derivatives of elementary functions using the algorithmic language {BCY}. ({Chinese})

entry:
@Article{Chen:1981:AFD,
  author =       "Gang Chen",
  title =        "An attempt to find the derivatives of elementary
                 functions using the algorithmic language {BCY}.
                 ({Chinese})",
  journal =      "Zhejiang Daxue Xuebao",
  volume =       "3",
  pages =        "141--149",
  year =         "1981",
  MRclass =      "26A09",
  MRnumber =     "714 524",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: elefunt.bib
label: Davis:1981:EFA
author: Diane F. Davis
title: Elementary Functions on an Array Processor
crossref: IEEE:1981:PIS
pages: 170--178
year: 1981
bibdate: Mon May 19 13:30:58 1997
bibtimestamp: 1997.05.19 13:30:58 ???
acknowledgement: ack-nhfb
rawauthor: Diane F. Davis
rawtitle: Elementary Functions on an Array Processor
bibsource:
ftp://ftp.ira.uka.de/pub/bibliography/Theory/arith.bib.gz; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@InProceedings{Davis:1981:EFA,
  author =       "Diane F. Davis",
  title =        "Elementary Functions on an Array Processor",
  crossref =     "IEEE:1981:PIS",
  pages =        "170--178",
  year =         "1981",
  bibdate =      "Mon May 19 13:30:58 1997",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Theory/arith.bib.gz;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Delahaye:1981:ACS
author: J.-P. Delahaye
journal: j-CALCOLO
volume: 18
number: 2
pages: 1--116
year: 1981
CODEN: CDABAE
DOI: https://doi.org/10.1007/BF02576491
ISSN: 0008-0624 (print), 1126-5434 (electronic) OR 00080624 (print), 11265434 (electronic)
ISSNL: 0008-0624 OR 00080624
MRclass: 65B05
MRnumber: 647821 (83a:65004)
bibdate: Thu Dec 1 17:36:45 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2011.12.01 17:36:45 ???
fjournal: Calcolo
keywords: convergence acceleration
language: French
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10092
rawauthor: J.-P. Delahaye
title:
Acceleration de la convergence des suites dont le rapport des erreurs est borne. (French) [Convergence acceleration for sequences with bounded error ratios]

rawtitle:
Acc{\'e}l{\'e}ration de la convergence des suites dont le rapport des erreurs est born{\'e}. ({French}) [{Convergence} acceleration for sequences with bounded error ratios]

entry:
@Article{Delahaye:1981:ACS,
  author =       "J.-P. Delahaye",
  title =        "Acc{\'e}l{\'e}ration de la convergence des suites dont
                 le rapport des erreurs est born{\'e}. ({French})
                 [{Convergence} acceleration for sequences with bounded
                 error ratios]",
  journal =      j-CALCOLO,
  volume =       "18",
  number =       "2",
  pages =        "1--116",
  year =         "1981",
  CODEN =        "CDABAE",
  DOI =          "https://doi.org/10.1007/BF02576491",
  ISSN =         "0008-0624 (print), 1126-5434 (electronic)",
  ISSN-L =       "0008-0624",
  MRclass =      "65B05",
  MRnumber =     "647821 (83a:65004)",
  bibdate =      "Thu Dec 1 17:36:45 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Calcolo",
  journal-URL =  "http://link.springer.com/journal/10092",
  keywords =     "convergence acceleration",
  language =     "{French}",
}


bibtype: article
filename: elefunt.bib
label: Drachman:1981:TTH
author: B. Drachman and C. I. Chuang
journal: j-J-COMPUT-APPL-MATH
volume: 7
number: 3
pages: 167--171
month: sep
monthnumber: 9
year: 1981
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 11:59:22 MST 2017
bibtimestamp: 2017.02.25 11:59:22 MST
URL: http://www.sciencedirect.com/science/article/pii/0771050X81900140
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: B. Drachman and C. I. Chuang
title:
A table of two hundred zeros of the derivative of the modified Bessel function $ K_n(z) $ and a graph of their distribution

bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1980.bib

rawtitle:
A table of two hundred zeros of the derivative of the modified {Bessel} function {$ K_n(z) $} and a graph of their distribution

entry:
@Article{Drachman:1981:TTH,
  author =       "B. Drachman and C. I. Chuang",
  title =        "A table of two hundred zeros of the derivative of the
                 modified {Bessel} function {$ K_n(z) $} and a graph of
                 their distribution",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "7",
  number =       "3",
  pages =        "167--171",
  month =        sep,
  year =         "1981",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 11:59:22 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1980.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0771050X81900140",
  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: Farmwald:1981:HBE
author: P. Michael Farmwald
title: High Bandwidth Evaluation of Elementary Functions
crossref: IEEE:1981:PIS
pages: 139--142
year: 1981
bibdate: Mon May 19 13:30:58 1997
bibtimestamp: 1997.05.19 13:30:58 ???
acknowledgement: ack-nhfb
rawauthor: P. Michael Farmwald
rawtitle: High Bandwidth Evaluation of Elementary Functions
bibsource:
ftp://ftp.ira.uka.de/pub/bibliography/Theory/arith.bib.gz; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@InProceedings{Farmwald:1981:HBE,
  author =       "P. Michael Farmwald",
  title =        "High Bandwidth Evaluation of Elementary Functions",
  crossref =     "IEEE:1981:PIS",
  pages =        "139--142",
  year =         "1981",
  bibdate =      "Mon May 19 13:30:58 1997",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Theory/arith.bib.gz;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Fettis:1981:TEHb
author: Henry E. Fettis
journal: j-MATH-COMPUT
volume: 36
number: 153
pages: 317--317
month: jan
monthnumber: 1
year: 1981
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 65A05
MRnumber: 82a:65008a
bibdate: Sat Apr 12 15:32:35 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.04.12 15:32:35 ???
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Henry E. Fettis
title:
Table errata: em Handbook of elliptic integrals for engineers and physicists [second edition, Springer, New York, 1971 and MR bf 43 #3506] by P. F. Byrd and M. D. Friedman

rawtitle:
Table errata: {{\em Handbook of elliptic integrals for engineers and physicists} [second edition, Springer, New York, 1971 and MR {\bf 43} \#3506] by P. F. Byrd and M. D. Friedman}

entry:
@Article{Fettis:1981:TEHb,
  author =       "Henry E. Fettis",
  title =        "Table errata: {{\em Handbook of elliptic integrals for
                 engineers and physicists} [second edition, Springer,
                 New York, 1971 and MR {\bf 43} \#3506] by P. F. Byrd
                 and M. D. Friedman}",
  journal =      j-MATH-COMPUT,
  volume =       "36",
  number =       "153",
  pages =        "317--317",
  month =        jan,
  year =         "1981",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65A05",
  MRnumber =     "82a:65008a",
  bibdate =      "Sat Apr 12 15:32:35 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Fettis:1981:TETb
author: Henry E. Fettis
journal: j-MATH-COMPUT
volume: 36
number: 153
pages: 318
month: jan
monthnumber: 1
year: 1981
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 318.65A05
MRnumber: 82a:65010
bibdate: Sat Jan 11 13:29:06 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 13:29:06 MST
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Henry E. Fettis
title:
Table errata: em A table of the complete elliptic integral of the first kind for complex values of the modulus, Part I [Rep. No. ARL 69-0172, Aerospace Res. Lab., Wright--Patterson Air Force Base, Ohio, 1969; MR bf 40 #6725] by Fettis and J. C. Caslin

rawtitle:
Table errata: {{\em A table of the complete elliptic integral of the first kind for complex values of the modulus, Part I} [Rep. No. ARL 69-0172, Aerospace Res. Lab., Wright--Patterson Air Force Base, Ohio, 1969; MR {\bf 40} \#6725] by Fettis and J. C. Caslin}

entry:
@Article{Fettis:1981:TETb,
  author =       "Henry E. Fettis",
  title =        "Table errata: {{\em A table of the complete elliptic
                 integral of the first kind for complex values of the
                 modulus, Part I} [Rep. No. ARL 69-0172, Aerospace Res.
                 Lab., Wright--Patterson Air Force Base, Ohio, 1969; MR
                 {\bf 40} \#6725] by Fettis and J. C. Caslin}",
  journal =      j-MATH-COMPUT,
  volume =       "36",
  number =       "153",
  pages =        "318",
  month =        jan,
  year =         "1981",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "318.65A05",
  MRnumber =     "82a:65010",
  bibdate =      "Sat Jan 11 13:29:06 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Fransen:1981:ACH
author: Arne Fransen
journal: j-MATH-COMPUT
volume: 37
number: 155
pages: 233--235
month: jul
monthnumber: 7
year: 1981
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 65A05 (65D20)
MRnumber: 82m:65002
bibdate: Sat Apr 01 10:12:58 2000
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 2000.04.01 10:12:58 ???
note: See cite Fransen:1980:HPV.
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Arne Frans{\'e}n
rawnote: See \cite{Fransen:1980:HPV}.
title:
Addendum and corrigendum to: ``High-precision values of the gamma function and of some related coefficients'' [Math. Comp. bf 34 (1980), no. 150, 553--566, MR 81f:65004] by Fransen and S. Wrigge

rawtitle:
Addendum and corrigendum to: {``High-precision values of the gamma function and of some related coefficients''} {[Math. Comp. {\bf 34} (1980), no. 150, 553--566, MR 81f:65004] by Frans{\'e}n and S. Wrigge}

entry:
@Article{Fransen:1981:ACH,
  author =       "Arne Frans{\'e}n",
  title =        "Addendum and corrigendum to: {``High-precision values
                 of the gamma function and of some related
                 coefficients''} {[Math. Comp. {\bf 34} (1980), no. 150,
                 553--566, MR 81f:65004] by Frans{\'e}n and S. Wrigge}",
  journal =      j-MATH-COMPUT,
  volume =       "37",
  number =       "155",
  pages =        "233--235",
  month =        jul,
  year =         "1981",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65A05 (65D20)",
  MRnumber =     "82m:65002",
  bibdate =      "Sat Apr 01 10:12:58 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  note =         "See \cite{Fransen:1980:HPV}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Fredette:1981:RES
author: G. Fredette
title: 68000 routine extracts square roots
journal: j-EDN
volume: 26
number: 16
pages: 185--194
month: aug
monthnumber: 8
year: 1981
CODEN: EDNSBH
ISSN: 0012-7515, 0364-6637 OR 00127515, 03646637
bibdate: Thu Sep 1 10:15:56 1994
bibtimestamp: 1994.09.01 10:15:56 ???
fjournal: EDN
acknowledgement: ack-nj
rawauthor: G. Fredette
rawtitle: 68000 routine extracts square roots
entry:
@Article{Fredette:1981:RES,
  author =       "G. Fredette",
  title =        "68000 routine extracts square roots",
  journal =      j-EDN,
  volume =       "26",
  number =       "16",
  pages =        "185--194",
  month =        aug,
  year =         "1981",
  CODEN =        "EDNSBH",
  ISSN =         "0012-7515, 0364-6637",
  bibdate =      "Thu Sep 1 10:15:56 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "EDN",
}


bibtype: techreport
filename: elefunt.bib
label: Fullerton:1981:FUMa
author: L. W. Fullerton
title: FNLIB User's Manual Explanatory Table of Contents
type: Technical report
number: CSTR 92
institution: inst-ATT-BELL
address: inst-ATT-BELL:adr
pages: 185--194
month: mar
monthnumber: 3
year: 1981
bibdate: Sat Feb 05 17:39:14 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.02.05 17:39:14 ???
acknowledgement: ack-nhfb
rawauthor: L. W. Fullerton
rawtitle: {FNLIB} User's Manual Explanatory Table of Contents
entry:
@TechReport{Fullerton:1981:FUMa,
  author =       "L. W. Fullerton",
  title =        "{FNLIB} User's Manual Explanatory Table of Contents",
  type =         "Technical report",
  number =       "CSTR 92",
  institution =  inst-ATT-BELL,
  address =      inst-ATT-BELL:adr,
  month =        mar,
  year =         "1981",
  bibdate =      "Sat Feb 05 17:39:14 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: techreport
filename: elefunt.bib
label: Fullerton:1981:FUMb
author: L. W. Fullerton
title: FNLIB User's Manual
type: Technical report
number: CSTR 95
institution: inst-ATT-BELL
address: inst-ATT-BELL:adr
pages: 185--194
month: mar
monthnumber: 3
year: 1981
bibdate: Sat Feb 05 17:39:14 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.02.05 17:39:14 ???
acknowledgement: ack-nhfb
rawauthor: L. W. Fullerton
rawtitle: {FNLIB} User's Manual
entry:
@TechReport{Fullerton:1981:FUMb,
  author =       "L. W. Fullerton",
  title =        "{FNLIB} User's Manual",
  type =         "Technical report",
  number =       "CSTR 95",
  institution =  inst-ATT-BELL,
  address =      inst-ATT-BELL:adr,
  month =        mar,
  year =         "1981",
  bibdate =      "Sat Feb 05 17:39:14 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Gasper:1981:SFB
author: George Gasper
title: Summation Formulas for Basic Hypergeometric Series
journal: j-SIAM-J-MATH-ANA
volume: 12
number: 2
pages: 196--200
month: mar
monthnumber: 3
year: 1981
CODEN: SJMAAH
ISSN: 0036-1410 (print), 1095-7154 (electronic) OR 00361410 (print), 10957154 (electronic)
ISSNL: 0036-1410 OR 00361410
MRclass: 33A30
MRnumber: 82a:33005
MRreviewer: L. J. Slater
bibdate: Sun Nov 28 19:22:39 MST 2010
bibtimestamp: 2010.11.28 19:22:39 MST
fjournal: SIAM Journal on Mathematical Analysis
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sima
rawauthor: George Gasper
rawtitle: Summation Formulas for Basic Hypergeometric Series
bibsource:
http://epubs.siam.org/sam-bin/dbq/toc/SIMA/12/2; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/siamjmathana.bib

entry:
@Article{Gasper:1981:SFB,
  author =       "George Gasper",
  title =        "Summation Formulas for Basic Hypergeometric Series",
  journal =      j-SIAM-J-MATH-ANA,
  volume =       "12",
  number =       "2",
  pages =        "196--200",
  month =        mar,
  year =         "1981",
  CODEN =        "SJMAAH",
  ISSN =         "0036-1410 (print), 1095-7154 (electronic)",
  ISSN-L =       "0036-1410",
  MRclass =      "33A30",
  MRnumber =     "82a:33005",
  MRreviewer =   "L. J. Slater",
  bibdate =      "Sun Nov 28 19:22:39 MST 2010",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMA/12/2;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjmathana.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Mathematical Analysis",
  journal-URL =  "http://epubs.siam.org/sima",
}


bibtype: article
filename: elefunt.bib
label: Gatto:1981:NEM
author: M. A. Gatto and J. B. Seery
title: Numerical evaluation of the modified Bessel functions $I$ and $K$
journal: j-COMPUT-MATH-APPL
volume: 7
number: 3
pages: 203--209
year: 1981
CODEN: CMAPDK
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Wed Mar 1 18:51:20 MST 2017
bibtimestamp: 2017.03.01 18:51:20 MST
URL: http://www.sciencedirect.com/science/article/pii/0898122181900808
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/08981221/
rawauthor: M. A. Gatto and J. B. Seery
rawtitle: Numerical evaluation of the modified {Bessel} functions {$I$} and {$K$}
bibsource:
https://www.math.utah.edu/pub/tex/bib/computmathappl1980.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Gatto:1981:NEM,
  author =       "M. A. Gatto and J. B. Seery",
  title =        "Numerical evaluation of the modified {Bessel}
                 functions {$I$} and {$K$}",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "7",
  number =       "3",
  pages =        "203--209",
  month =        "????",
  year =         "1981",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 18:51:20 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0898122181900808",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221/",
}


bibtype: article
filename: elefunt.bib
label: Glasser:1981:CBS
author: M. L. Glasser
title: A Class of Bessel Summations
journal: j-MATH-COMPUT
volume: 37
number: 156
pages: 499--501
month: oct
monthnumber: 10
year: 1981
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 33A40 (42A16 44A15)
MRnumber: 82j:33015
MRreviewer: B. D. Agrawal
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
keywords: Bessel functions; Bessel summations; infinite series
acknowledgement: ack-nhfb
classcodes: B0220 (Mathematical analysis); C1120 (Mathematical analysis)
corpsource: Dept. of Math. and Computer Sci., Clarkson Coll., Potsdam, NY, USA
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: M. L. Glasser
rawtitle: A Class of {Bessel} Summations
entry:
@Article{Glasser:1981:CBS,
  author =       "M. L. Glasser",
  title =        "A Class of {Bessel} Summations",
  journal =      j-MATH-COMPUT,
  volume =       "37",
  number =       "156",
  pages =        "499--501",
  month =        oct,
  year =         "1981",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "33A40 (42A16 44A15)",
  MRnumber =     "82j:33015",
  MRreviewer =   "B. D. Agrawal",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0220 (Mathematical analysis); C1120 (Mathematical
                 analysis)",
  corpsource =   "Dept. of Math. and Computer Sci., Clarkson Coll.,
                 Potsdam, NY, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Bessel functions; Bessel summations; infinite series",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Haavie:1981:RUT
author: Tore Haa vie
title: Remarks on a unified theory for classical and generalized interpolation and extrapolation
journal: j-BIT
volume: 21
number: 4
pages: 465--474
month: dec
monthnumber: 12
year: 1981
CODEN: BITTEL, NBITAB
DOI: https://doi.org/10.1007/BF01932843
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
ISSNL: 0006-3835 OR 00063835
MRclass: 41A05 (65D05)
MRnumber: 83d:41004
MRreviewer: G. M{\"u}hlbach
bibdate: Wed Jan 4 18:52:17 MST 2006
bibtimestamp: 2006.01.04 18:52:17 MST
URL: http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=21&issue=4&spage=465
fjournal: BIT (Nordisk tidskrift for informationsbehandling)
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10543
rawauthor: Tore H{\aa}vie
rawtitle: Remarks on a unified theory for classical and generalized interpolation and extrapolation
bibsource:
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=21&issue=4; https://www.math.utah.edu/pub/tex/bib/bit.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Haavie:1981:RUT,
  author =       "Tore H{\aa}vie",
  title =        "Remarks on a unified theory for classical and
                 generalized interpolation and extrapolation",
  journal =      j-BIT,
  volume =       "21",
  number =       "4",
  pages =        "465--474",
  month =        dec,
  year =         "1981",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01932843",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "41A05 (65D05)",
  MRnumber =     "83d:41004",
  MRreviewer =   "G. M{\"u}hlbach",
  bibdate =      "Wed Jan 4 18:52:17 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=21&issue=4;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=21&issue=4&spage=465",
  acknowledgement = ack-nhfb,
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}


bibtype: article
filename: elefunt.bib
label: Hill:1981:RSD
author: G. W. Hill
title: Remark on ``Algorithm 395: Student's $t$-Distribution''
journal: j-TOMS
volume: 7
number: 2
pages: 247--249
month: jun
monthnumber: 6
year: 1981
CODEN: ACMSCU
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Tue Feb 06 05:28:18 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1996.02.06 05:28:18 ???
note: See cite Hill:1970:AASa,Hill:1970:AASb,elLozy:1979:RAS.
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: G. W. Hill
rawnote: See \cite{Hill:1970:AASa,Hill:1970:AASb,elLozy:1979:RAS}.
rawtitle: Remark on ``{Algorithm 395: Student's $t$-Distribution}''
entry:
@Article{Hill:1981:RSD,
  author =       "G. W. Hill",
  title =        "Remark on ``{Algorithm 395: Student's
                 $t$-Distribution}''",
  journal =      j-TOMS,
  volume =       "7",
  number =       "2",
  pages =        "247--249",
  month =        jun,
  year =         "1981",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Feb 06 05:28:18 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See
                 \cite{Hill:1970:AASa,Hill:1970:AASb,elLozy:1979:RAS}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: article
filename: elefunt.bib
label: Hill:1981:RSQ
author: G. W. Hill
title: Remark on ``Algorithm 396: Student's $t$-Quantiles''
journal: j-TOMS
volume: 7
number: 2
pages: 250--251
month: jun
monthnumber: 6
year: 1981
CODEN: ACMSCU
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Tue Feb 06 05:28:19 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1996.02.06 05:28:19 ???
note: See cite Hill:1970:AASb.
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: G. W. Hill
rawnote: See \cite{Hill:1970:AASb}.
rawtitle: Remark on ``{Algorithm 396: Student's $t$-Quantiles}''
entry:
@Article{Hill:1981:RSQ,
  author =       "G. W. Hill",
  title =        "Remark on ``{Algorithm 396: Student's
                 $t$-Quantiles}''",
  journal =      j-TOMS,
  volume =       "7",
  number =       "2",
  pages =        "250--251",
  month =        jun,
  year =         "1981",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Feb 06 05:28:19 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Hill:1970:AASb}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: article
filename: elefunt.bib
label: Hough:1981:API
author: D. Hough
title: Application of the proposed IEEE 754 standard for floating-point arithmetic
journal: j-COMPUTER
volume: 14
number: 3
pages: 70--74
year: 1981
CODEN: CPTRB4
ISSN: 0018-9162 (print), 1558-0814 (electronic) OR 00189162 (print), 15580814 (electronic)
ISSNL: 0018-9162 OR 00189162
bibdate: Mon May 19 13:30:58 1997
bibtimestamp: 1997.05.19 13:30:58 ???
fjournal: Computer
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2
rawauthor: D. Hough
rawtitle: Application of the proposed {IEEE 754} standard for floating-point arithmetic
bibsource:
ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD/1981.bib.gz; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

annote:
Various features of the proposed standard provide an especially convenient environment for programming numerical procedures such as the familiar elementary functions.

entry:
@Article{Hough:1981:API,
  author =       "D. Hough",
  title =        "Application of the proposed {IEEE 754} standard for
                 floating-point arithmetic",
  journal =      j-COMPUTER,
  volume =       "14",
  number =       "3",
  pages =        "70--74",
  year =         "1981",
  CODEN =        "CPTRB4",
  ISSN =         "0018-9162 (print), 1558-0814 (electronic)",
  ISSN-L =       "0018-9162",
  bibdate =      "Mon May 19 13:30:58 1997",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD/1981.bib.gz;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  annote =       "Various features of the proposed standard provide an
                 especially convenient environment for programming
                 numerical procedures such as the familiar elementary
                 functions.",
  bydate =       "MB",
  byrev =        "Le",
  country =      "USA",
  date =         "14/06/82",
  descriptors =  "Computer arithmetic; floating point; computation
                 structure; method; application; standard",
  enum =         "1418",
  fjournal =     "Computer",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
  location =     "RWTH-AC-DFV: Bibl.",
  references =   "10",
  revision =     "21/04/91",
}


bibtype: article
filename: elefunt.bib
label: Iserles:1981:ARA
author: A. Iserles and M. J. D. Powell
title: On the $A$-acceptability of rational approximations that interpolate the exponential function
journal: j-IMA-J-NUMER-ANAL
volume: 1
number: 3
pages: 241--251
month: jul
monthnumber: 7
year: 1981
CODEN: IJNADH
DOI: https://doi.org/10.1093/imanum/1.3.241
ISSN: 0272-4979 (print), 1464-3642 (electronic) OR 02724979 (print), 14643642 (electronic)
ISSNL: 0272-4979 OR 02724979
MRclass: 65D15 (30E10)
MRnumber: 83a:65015 (641308)
bibdate: Sat Dec 23 17:06:35 MST 2000
bibtimestamp: 2000.12.23 17:06:35 MST
fjournal: IMA Journal of Numerical Analysis
acknowledgement: ack-nhfb
authordates: Michael James David Powell (29 July 1936--19 April 2015)
journalURL: http://imajna.oxfordjournals.org/content/by/year
rawauthor: A. Iserles and M. J. D. Powell
rawtitle: On the {$A$}-acceptability of rational approximations that interpolate the exponential function
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/p/powell-m-j-d.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/imajnumeranal.bib; MathSciNet database

entry:
@Article{Iserles:1981:ARA,
  author =       "A. Iserles and M. J. D. Powell",
  title =        "On the {$A$}-acceptability of rational approximations
                 that interpolate the exponential function",
  journal =      j-IMA-J-NUMER-ANAL,
  volume =       "1",
  number =       "3",
  pages =        "241--251",
  month =        jul,
  year =         "1981",
  CODEN =        "IJNADH",
  DOI =          "https://doi.org/10.1093/imanum/1.3.241",
  ISSN =         "0272-4979 (print), 1464-3642 (electronic)",
  ISSN-L =       "0272-4979",
  MRclass =      "65D15 (30E10)",
  MRnumber =     "83a:65015 (641308)",
  bibdate =      "Sat Dec 23 17:06:35 MST 2000",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/p/powell-m-j-d.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/imajnumeranal.bib;
                 MathSciNet database",
  acknowledgement = ack-nhfb,
  author-dates = "Michael James David Powell (29 July 1936--19 April
                 2015)",
  fjournal =     "IMA Journal of Numerical Analysis",
  journal-URL =  "http://imajna.oxfordjournals.org/content/by/year",
}


bibtype: article
filename: elefunt.bib
label: James:1981:LTS
author: D. G. James
title: Linear transformations of the second elementary function
journal: j-LIN-AND-MULT-ALGEBRA
volume: 10
number: 4
pages: 347--349
year: 1981
CODEN: LNMLAZ
ISSN: 0308-1087 (print), 1563-5139 (electronic) OR 03081087 (print), 15635139 (electronic)
ISSNL: 0308-1087 OR 03081087
MRclass: 15A69 (10C15)
MRnumber: 83c:15023
MRreviewer: E. W. Ellers
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
fjournal: Linear and Multilinear Algebra
acknowledgement: ack-nhfb
journalURL: http://www.tandfonline.com/loi/glma20
rawauthor: D. G. James
rawtitle: Linear transformations of the second elementary function
entry:
@Article{James:1981:LTS,
  author =       "D. G. James",
  title =        "Linear transformations of the second elementary
                 function",
  journal =      j-LIN-AND-MULT-ALGEBRA,
  volume =       "10",
  number =       "4",
  pages =        "347--349",
  year =         "1981",
  CODEN =        "LNMLAZ",
  ISSN =         "0308-1087 (print), 1563-5139 (electronic)",
  ISSN-L =       "0308-1087",
  MRclass =      "15A69 (10C15)",
  MRnumber =     "83c:15023",
  MRreviewer =   "E. W. Ellers",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear and Multilinear Algebra",
  journal-URL =  "http://www.tandfonline.com/loi/glma20",
}


bibtype: article
filename: elefunt.bib
label: Kunz:1981:QZ
author: W. Kunz
title: Quadratwurzel mit dem $ mu $P Z80 toenglish Square Roots with the Z80 Microprocessor endtoenglish
journal: j-ELECTRONIK
volume: 7
pages: 109--110
year: 1981
CODEN: EKRKAR
ISSN: 0013-5658 OR 00135658
bibdate: Fri Sep 16 16:30:41 1994
bibtimestamp: 1994.09.16 16:30:41 ???
fjournal: Elektronik
acknowledgement: ack-nj
rawauthor: W. Kunz
rawtitle:
{Quadratwurzel mit dem $ \mu $P Z80} \toenglish {Square Roots with the Z80 Microprocessor} \endtoenglish

entry:
@Article{Kunz:1981:QZ,
  author =       "W. Kunz",
  title =        "{Quadratwurzel mit dem $ \mu $P Z80} \toenglish
                 {Square Roots with the Z80 Microprocessor}
                 \endtoenglish",
  journal =      j-ELECTRONIK,
  volume =       "7",
  pages =        "109--110",
  year =         "1981",
  CODEN =        "EKRKAR",
  ISSN =         "0013-5658",
  bibdate =      "Fri Sep 16 16:30:41 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Elektronik",
}


bibtype: book
filename: elefunt.bib
label: Lewin:1981:PAF
author: Leonard Lewin
title: Polylogarithms and Associated Functions
publisher: pub-NORTH-HOLLAND
address: pub-NORTH-HOLLAND:adr
pages: xvii + 359
year: 1981
ISBN: 0-444-00550-1 OR 0444005501
ISBN13: 978-0-444-00550-2 OR 9780444005502
LCCN: QA342 .L47
bibdate: Fri Jun 16 13:56:23 MDT 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2023.06.16 13:56:23 MDT
remark: Lightly revised and retitled edition of cite Lewin:1958:DAF.
subject: Logarithmic functions
acknowledgement: ack-nhfb
authordates: 22-Jul-1919--13-Aug-2007
rawauthor: Leonard Lewin
rawtitle: Polylogarithms and Associated Functions
entry:
@Book{Lewin:1981:PAF,
  author =       "Leonard Lewin",
  title =        "Polylogarithms and Associated Functions",
  publisher =    pub-NORTH-HOLLAND,
  address =      pub-NORTH-HOLLAND:adr,
  pages =        "xvii + 359",
  year =         "1981",
  ISBN =         "0-444-00550-1",
  ISBN-13 =      "978-0-444-00550-2",
  LCCN =         "QA342 .L47",
  bibdate =      "Fri Jun 16 13:56:23 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  author-dates = "22-Jul-1919--13-Aug-2007",
  author-url =   "https://en.wikipedia.org/wiki/Leonard_Lewin_(telecommunications_engineer)",
  remark =       "Lightly revised and retitled edition of
                 \cite{Lewin:1958:DAF}.",
  subject =      "Logarithmic functions",
}


bibtype: incollection
filename: elefunt.bib
label: Longman:1981:DCA
author: I. M. Longman
booktitle: Pade approximation and its applications, Amsterdam 1980 (Amsterdam, 1980)
title: Difficulties of convergence acceleration
volume: 888
publisher: pub-SV
address: pub-SV:adr
pages: 273--289
year: 1981
MRclass: 65B10
MRnumber: 649102 (83d:65013)
bibdate: Thu Dec 1 17:36:45 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2011.12.01 17:36:45 ???
series: Lecture Notes in Mathematics
keywords: convergence acceleration
acknowledgement: ack-nhfb
rawauthor: I. M. Longman
rawbooktitle: {Pad{\'e} approximation and its applications, Amsterdam 1980 (Amsterdam, 1980)}
rawtitle: Difficulties of convergence acceleration
entry:
@InCollection{Longman:1981:DCA,
  author =       "I. M. Longman",
  booktitle =    "{Pad{\'e} approximation and its applications,
                 Amsterdam 1980 (Amsterdam, 1980)}",
  title =        "Difficulties of convergence acceleration",
  volume =       "888",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "273--289",
  year =         "1981",
  MRclass =      "65B10",
  MRnumber =     "649102 (83d:65013)",
  bibdate =      "Thu Dec 1 17:36:45 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Lecture Notes in Mathematics",
  acknowledgement = ack-nhfb,
  keywords =     "convergence acceleration",
}


bibtype: article
filename: elefunt.bib
label: Maino:1981:CPC
author: G. Maino and E. Menapace and A. Ventura
title: Computation of parabolic cylinder functions by means of a Tricomi expansion
journal: j-J-COMPUT-PHYS
volume: 40
number: 2
pages: 294--304
month: apr
monthnumber: 4
year: 1981
CODEN: JCTPAH
DOI: https://doi.org/10.1016/0021-9991(81)90211-4
ISSN: 0021-9991 (print), 1090-2716 (electronic) OR 00219991 (print), 10902716 (electronic)
ISSNL: 0021-9991 OR 00219991
bibdate: Sun Jan 1 15:59:06 MST 2012
bibtimestamp: 2012.01.01 15:59:06 MST
URL: http://www.sciencedirect.com/science/article/pii/0021999181902114
fjournal: Journal of Computational Physics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00219991/
rawauthor: G. Maino and E. Menapace and A. Ventura
rawtitle: Computation of parabolic cylinder functions by means of a {Tricomi} expansion
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jcomputphys1980.bib

entry:
@Article{Maino:1981:CPC,
  author =       "G. Maino and E. Menapace and A. Ventura",
  title =        "Computation of parabolic cylinder functions by means
                 of a {Tricomi} expansion",
  journal =      j-J-COMPUT-PHYS,
  volume =       "40",
  number =       "2",
  pages =        "294--304",
  month =        apr,
  year =         "1981",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(81)90211-4",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Sun Jan 1 15:59:06 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1980.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0021999181902114",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}


bibtype: article
filename: elefunt.bib
label: Markov:1981:ICE
author: S. M. Markov
title: On the interval computation of elementary functions
journal: j-C-R-ACAD-BULGARE-SCI
volume: 34
number: 3
pages: 319--322
year: 1981
CODEN: DBANAD
ISSN: 0366-8681 OR 03668681
MRclass: 65G10
MRnumber: 83e:65084
MRreviewer: David F. Griffiths
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
fjournal: Comptes rendus de l'Academie bulgare des sciences
acknowledgement: ack-nhfb
rawauthor: S. M. Markov
rawtitle: On the interval computation of elementary functions
entry:
@Article{Markov:1981:ICE,
  author =       "S. M. Markov",
  title =        "On the interval computation of elementary functions",
  journal =      j-C-R-ACAD-BULGARE-SCI,
  volume =       "34",
  number =       "3",
  pages =        "319--322",
  year =         "1981",
  CODEN =        "DBANAD",
  ISSN =         "0366-8681",
  MRclass =      "65G10",
  MRnumber =     "83e:65084",
  MRreviewer =   "David F. Griffiths",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Comptes rendus de l'Acad{\'e}mie bulgare des
                 sciences",
}


bibtype: article
filename: elefunt.bib
label: McCullagh:1981:RCS
author: Peter McCullagh
title: A rapidly convergent series for computing $ psi (z) $ and its derivatives
journal: j-MATH-COMPUT
volume: 36
number: 153
pages: 247--248
month: jan
monthnumber: 1
year: 1981
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 65D20 (33A15)
MRnumber: 81m:65028
MRreviewer: J. Gregor
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
URL: http://www.jstor.org/stable/2007741
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
classcodes: C4120 (Functional analysis)
corpsource: Imperial Coll. of Sci. and Technol., London, UK
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: Peter McCullagh
rawtitle: A rapidly convergent series for computing $ \psi (z) $ and its derivatives
keywords:
(mathematics); convergence; function evaluation; log gamma function; poles; poles and zeros; rapidly convergent series; series; series expansion; uniformly convergent

entry:
@Article{McCullagh:1981:RCS,
  author =       "Peter McCullagh",
  title =        "A rapidly convergent series for computing $ \psi (z) $
                 and its derivatives",
  journal =      j-MATH-COMPUT,
  volume =       "36",
  number =       "153",
  pages =        "247--248",
  month =        jan,
  year =         "1981",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65D20 (33A15)",
  MRnumber =     "81m:65028",
  MRreviewer =   "J. Gregor",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  URL =          "http://www.jstor.org/stable/2007741",
  acknowledgement = ack-nhfb,
  classcodes =   "C4120 (Functional analysis)",
  corpsource =   "Imperial Coll. of Sci. and Technol., London, UK",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "(mathematics); convergence; function evaluation; log
                 gamma function; poles; poles and zeros; rapidly
                 convergent series; series; series expansion; uniformly
                 convergent",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Moon:1981:AFC
author: Wooil Moon
title: Airy function with complex arguments
journal: j-COMP-PHYS-COMM
volume: 22
number: 4
pages: 411--417
month: may
monthnumber: 5
year: 1981
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/0010-4655(81)90138-7
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Mon Feb 13 09:27:06 MST 2012
bibtimestamp: 2012.02.13 09:27:06 MST
URL: http://www.sciencedirect.com/science/article/pii/0010465581901387
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: Wooil Moon
rawtitle: {Airy} function with complex arguments
bibsource:
https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Moon:1981:AFC,
  author =       "Wooil Moon",
  title =        "{Airy} function with complex arguments",
  journal =      j-COMP-PHYS-COMM,
  volume =       "22",
  number =       "4",
  pages =        "411--417",
  month =        may,
  year =         "1981",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(81)90138-7",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Feb 13 09:27:06 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0010465581901387",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}


bibtype: techreport
filename: elefunt.bib
label: Morris:1981:NDL
author: Alfred H. Morris, Jr.
title: NSWC / DL Library of Mathematics Subroutines
type: Report
number: NSWC/TR-79-338
institution: Naval Surface Warfare Center
address: Dahlgren, VA 22448-5000, USA; Silver Spring, MD 20903-5000, USA
pages: 235
year: 1981
bibdate: Tue Jun 13 08:47:19 2023
bibtimestamp: 2023.06.13 08:47:19 ???
note: See also later editions cite Morris:1990:NLM,Morris:1993:NLM.
URL: https://ntrl.ntis.gov/NTRL/dashboard/searchResults/titleDetail/ADA108106.xhtml
acknowledgement: ack-nhfb
rawauthor: Alfred H. {Morris, Jr.}
rawnote: See also later editions \cite{Morris:1990:NLM,Morris:1993:NLM}.
rawtitle: {NSWC\slash DL} Library of Mathematics Subroutines
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fortran2.bib

abstract:
The NSWC/DL library is a library of general-purpose FORTRAN subroutines that provide a basic computational capability in a variety of mathematical activities. Although intended for use on the CDC 6000 series computers, emphasis has been placed on the transportability of the codes. Subroutines are available in the following areas: Elementary Operations, Geometry, Special Functions, Polynomials, Solutions of Nonlinear Equations, Vectors, Matrices, Sparse Matrices, Eigenvalues and Eigenvectors, Least Squares Solutions of Linear Equations, Optimization, Transforms, Approximation of Functions, Curve Fitting, Surface Fitting over Rectangular Grids, Surface Fitting over Arbitrarily Positioned Data Points, Numerical Integration, Ordinary Differential Equations/Initial Value Problems, and Random Number Generation.

rawabstract:
The NSWC/DL library is a library of general-purpose FORTRAN subroutines that provide a basic computational capability in a variety of mathematical activities. Although intended for use on the CDC 6000 series computers, emphasis has been placed on the transportability of the codes. Subroutines are available in the following areas: Elementary Operations, Geometry, Special Functions, Polynomials, Solutions of Nonlinear Equations, Vectors, Matrices, Sparse Matrices, Eigenvalues and Eigenvectors, Least Squares Solutions of Linear Equations, Optimization, Transforms, Approximation of Functions, Curve Fitting, Surface Fitting over Rectangular Grids, Surface Fitting over Arbitrarily Positioned Data Points, Numerical Integration, Ordinary Differential Equations/Initial Value Problems, and Random Number Generation.

entry:
@TechReport{Morris:1981:NDL,
  author =       "Alfred H. {Morris, Jr.}",
  title =        "{NSWC\slash DL} Library of Mathematics Subroutines",
  type =         "Report",
  number =       "NSWC/TR-79-338",
  institution =  "Naval Surface Warfare Center",
  address =      "Dahlgren, VA 22448-5000, USA; Silver Spring, MD
                 20903-5000, USA",
  pages =        "235",
  year =         "1981",
  bibdate =      "Tue Jun 13 08:47:19 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fortran2.bib",
  note =         "See also later editions
                 \cite{Morris:1990:NLM,Morris:1993:NLM}.",
  URL =          "https://ntrl.ntis.gov/NTRL/dashboard/searchResults/titleDetail/ADA108106.xhtml",
  abstract =     "The NSWC/DL library is a library of general-purpose
                 FORTRAN subroutines that provide a basic computational
                 capability in a variety of mathematical activities.
                 Although intended for use on the CDC 6000 series
                 computers, emphasis has been placed on the
                 transportability of the codes. Subroutines are
                 available in the following areas: Elementary
                 Operations, Geometry, Special Functions, Polynomials,
                 Solutions of Nonlinear Equations, Vectors, Matrices,
                 Sparse Matrices, Eigenvalues and Eigenvectors, Least
                 Squares Solutions of Linear Equations, Optimization,
                 Transforms, Approximation of Functions, Curve Fitting,
                 Surface Fitting over Rectangular Grids, Surface Fitting
                 over Arbitrarily Positioned Data Points, Numerical
                 Integration, Ordinary Differential Equations/Initial
                 Value Problems, and Random Number Generation.",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: elefunt.bib
label: Peng:1981:AES
author: Hong Peng
title: Algorithms for extracting square roots and cube roots
crossref: IEEE:1981:PSC
pages: 121--126
year: 1981
bibdate: Thu Sep 01 11:37:17 1994
bibtimestamp: 1994.09.01 11:37:17 ???
URL: http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Peng.pdf
keywords: ARITH-5
acknowledgement: ack-nj
rawauthor: Hong Peng
rawtitle: Algorithms for extracting square roots and cube roots
abstract:
This paper describes a kind of algorithms for fast extracting square roots and cube roots, their mathematical proofs, their revised algorithm formulae, and hardware implementation of the square root algorithm. These algorithms may be of no significance for large scale computer with fast division. But I am sure that it is effective and economical to apply these algorithms to the circuit designs of some mini- and microcomputers with general multiplication and division, such as nonrestoring division.

rawabstract:
This paper describes a kind of algorithms for fast extracting square roots and cube roots, their mathematical proofs, their revised algorithm formulae, and hardware implementation of the square root algorithm. These algorithms may be of no significance for large scale computer with fast division. But I am sure that it is effective and economical to apply these algorithms to the circuit designs of some mini- and microcomputers with general multiplication and division, such as nonrestoring division.

entry:
@InProceedings{Peng:1981:AES,
  author =       "Hong Peng",
  title =        "Algorithms for extracting square roots and cube
                 roots",
  crossref =     "IEEE:1981:PSC",
  pages =        "121--126",
  year =         "1981",
  bibdate =      "Thu Sep 01 11:37:17 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Peng.pdf",
  abstract =     "This paper describes a kind of algorithms for fast
                 extracting square roots and cube roots, their
                 mathematical proofs, their revised algorithm formulae,
                 and hardware implementation of the square root
                 algorithm. These algorithms may be of no significance
                 for large scale computer with fast division. But I am
                 sure that it is effective and economical to apply these
                 algorithms to the circuit designs of some mini- and
                 microcomputers with general multiplication and
                 division, such as nonrestoring division.",
  acknowledgement = ack-nj,
  keywords =     "ARITH-5",
}


bibtype: article
filename: elefunt.bib
label: Razaz:1981:RAF
author: M. Razaz and J. L. Schonfelder
title: Remark on ``Algorithm 498: Airy Functions Using Chebyshev Series Approximations''
journal: j-TOMS
volume: 7
number: 3
pages: 404--405
month: sep
monthnumber: 9
year: 1981
CODEN: ACMSCU
DOI: https://doi.org/10.1145/355958.355971
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Tue Aug 30 00:28:07 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.08.30 00:28:07 ???
note: See cite Prince:1975:AAF.
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: M. Razaz and J. L. Schonfelder
rawnote: See \cite{Prince:1975:AAF}.
rawtitle: Remark on ``{Algorithm} 498: {Airy} Functions Using {Chebyshev} Series Approximations''
entry:
@Article{Razaz:1981:RAF,
  author =       "M. Razaz and J. L. Schonfelder",
  title =        "Remark on ``{Algorithm} 498: {Airy} Functions Using
                 {Chebyshev} Series Approximations''",
  journal =      j-TOMS,
  volume =       "7",
  number =       "3",
  pages =        "404--405",
  month =        sep,
  year =         "1981",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355958.355971",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 30 00:28:07 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Prince:1975:AAF}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: article
filename: elefunt.bib
label: Schulten:1981:NAE
author: Z. Schulten and R. G. Gordon and D. G. M. Anderson
journal: j-J-COMPUT-PHYS
volume: 42
number: 2
pages: 213--237
month: aug
monthnumber: 8
year: 1981
CODEN: JCTPAH
DOI: https://doi.org/10.1016/0021-9991(81)90241-2
ISSN: 0021-9991 (print), 1090-2716 (electronic) OR 00219991 (print), 10902716 (electronic)
ISSNL: 0021-9991 OR 00219991
bibdate: Sun Jan 1 15:59:07 MST 2012
bibtimestamp: 2012.01.01 15:59:07 MST
URL: http://www.sciencedirect.com/science/article/pii/0021999181902412
fjournal: Journal of Computational Physics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00219991/
rawauthor: Z. Schulten and R. G. Gordon and D. G. M. Anderson
title:
A numerical algorithm for the evaluation of Weber parabolic cylinder functions $ U(a, x) $, $ V(a, x) $, and $ W(a, pm x) $

rawtitle:
A numerical algorithm for the evaluation of {Weber} parabolic cylinder functions {$ U(a, x) $}, {$ V(a, x) $}, and {$ W(a, \pm x) $}

entry:
@Article{Schulten:1981:NAE,
  author =       "Z. Schulten and R. G. Gordon and D. G. M. Anderson",
  title =        "A numerical algorithm for the evaluation of {Weber}
                 parabolic cylinder functions {$ U(a, x) $}, {$ V(a, x)
                 $}, and {$ W(a, \pm x) $}",
  journal =      j-J-COMPUT-PHYS,
  volume =       "42",
  number =       "2",
  pages =        "213--237",
  month =        aug,
  year =         "1981",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(81)90241-2",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Sun Jan 1 15:59:07 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1980.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0021999181902412",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}


bibtype: article
filename: elefunt.bib
label: Shepherd:1981:CA
author: M. M. Shepherd and J. G. Laframboise
title: Chebyshev Approximation of $ (1 + 2 x) exp (x^2) erfc (x) $ in $ 0 leq x < infty $
journal: j-MATH-COMPUT
volume: 36
number: 153
pages: 249--253
month: jan
monthnumber: 1
year: 1981
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 65D20
MRnumber: 83c:65029
MRreviewer: John P. Coleman
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
keywords: (1+2x)exp(x/sup 2/)erfc x; Chebyshev approximation; Chebyshev expansion; erfc x; single
acknowledgement: ack-nhfb
classcodes: C4130 (Interpolation and function approximation)
corpsource: York Univ., Toronto, Ont., Canada
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: M. M. Shepherd and J. G. Laframboise
rawtitle: {Chebyshev} Approximation of $ (1 + 2 x) \exp (x^2) \erfc (x) $ in $ 0 \leq x < \infty $
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib; JSTOR database

entry:
@Article{Shepherd:1981:CA,
  author =       "M. M. Shepherd and J. G. Laframboise",
  title =        "{Chebyshev} Approximation of $ (1 + 2 x) \exp (x^2)
                 \erfc (x) $ in $ 0 \leq x < \infty $",
  journal =      j-MATH-COMPUT,
  volume =       "36",
  number =       "153",
  pages =        "249--253",
  month =        jan,
  year =         "1981",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65D20",
  MRnumber =     "83c:65029",
  MRreviewer =   "John P. Coleman",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "C4130 (Interpolation and function approximation)",
  corpsource =   "York Univ., Toronto, Ont., Canada",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "(1+2x)exp(x/sup 2/)erfc x; Chebyshev approximation;
                 Chebyshev expansion; erfc x; single",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Smith:1981:ERA
author: J. M. Smith and F. W. J. Olver and D. W. Lozier
title: Extended-Range Arithmetic and Normalized Legendre Polynomials
journal: j-TOMS
volume: 7
number: 1
pages: 93--105
month: mar
monthnumber: 3
year: 1981
CODEN: ACMSCU
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
MRclass: 65D20 (65G05)
MRnumber: 83a:65017
bibdate: Mon Aug 29 22:02:12 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.08.29 22:02:12 ???
URL: http://doi.acm.org/10.1145/355934.355940
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: angular momentum; extended-range arithmetic; Legendre polynomials; overflow; underflow
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: J. M. Smith and F. W. J. Olver and D. W. Lozier
rawtitle: Extended-Range Arithmetic and Normalized {Legendre} Polynomials
entry:
@Article{Smith:1981:ERA,
  author =       "J. M. Smith and F. W. J. Olver and D. W. Lozier",
  title =        "Extended-Range Arithmetic and Normalized {Legendre}
                 Polynomials",
  journal =      j-TOMS,
  volume =       "7",
  number =       "1",
  pages =        "93--105",
  month =        mar,
  year =         "1981",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D20 (65G05)",
  MRnumber =     "83a:65017",
  bibdate =      "Mon Aug 29 22:02:12 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://doi.acm.org/10.1145/355934.355940",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "angular momentum; extended-range arithmetic; Legendre
                 polynomials; overflow; underflow",
}


bibtype: article
filename: elefunt.bib
label: Steinberg:1981:LSE
author: D. Steinberg and M. Rodeh
title: A layout for the shuffle-exchange network with $ O(N^2 / log ^3 / 2N) $ area
journal: j-IEEE-TRANS-COMPUT
volume: C-30
number: 12
pages: 977--982
month: dec
monthnumber: 12
year: 1981
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1981.1675738
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Fri Nov 8 18:01:57 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2002.11.08 18:01:57 MST
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: D. Steinberg and M. Rodeh
rawtitle: A layout for the shuffle-exchange network with {$ O(N^2 / \log^{3 / 2N}) $} area
subject:
C. Computer Systems Organization; C.1 PROCESSOR ARCHITECTURES; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS

entry:
@Article{Steinberg:1981:LSE,
  author =       "D. Steinberg and M. Rodeh",
  title =        "A layout for the shuffle-exchange network with {$
                 O(N^2 / \log^{3 / 2N}) $} area",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-30",
  number =       "12",
  pages =        "977--982",
  month =        dec,
  year =         "1981",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1981.1675738",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  catcode =      "C.1.2; G.1.2",
  CRclass =      "C.1.2 Multiple Data Stream Architectures
                 (Multiprocessors); C.1.2 Interconnection architectures;
                 G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Computer Systems Organization, PROCESSOR
                 ARCHITECTURES, Multiple Data Stream Architectures
                 (Multiprocessors), Interconnection architectures;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation",
  fjournal =     "IEEE Transactions on Computers",
  genterm =      "design",
  guideno =      "06519",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  jrldate =      "Dec. 1981",
  subject =      "C. Computer Systems Organization; C.1 PROCESSOR
                 ARCHITECTURES; G. Mathematics of Computing; G.1
                 NUMERICAL ANALYSIS",
}


bibtype: article
filename: elefunt.bib
label: Steinhardt:1981:ASF
author: Paul J. Steinhardt and P. Chaudhari
title: Airy stress function for atomic models
journal: j-J-COMPUT-PHYS
volume: 42
number: 2
pages: 266--276
month: aug
monthnumber: 8
year: 1981
CODEN: JCTPAH
DOI: https://doi.org/10.1016/0021-9991(81)90244-8
ISSN: 0021-9991 (print), 1090-2716 (electronic) OR 00219991 (print), 10902716 (electronic)
ISSNL: 0021-9991 OR 00219991
bibdate: Sun Jan 1 15:59:07 MST 2012
bibtimestamp: 2012.01.01 15:59:07 MST
URL: http://www.sciencedirect.com/science/article/pii/0021999181902448
fjournal: Journal of Computational Physics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00219991/
rawauthor: Paul J. Steinhardt and P. Chaudhari
rawtitle: {Airy} stress function for atomic models
entry:
@Article{Steinhardt:1981:ASF,
  author =       "Paul J. Steinhardt and P. Chaudhari",
  title =        "{Airy} stress function for atomic models",
  journal =      j-J-COMPUT-PHYS,
  volume =       "42",
  number =       "2",
  pages =        "266--276",
  month =        aug,
  year =         "1981",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(81)90244-8",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Sun Jan 1 15:59:07 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1980.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0021999181902448",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}


bibtype: inproceedings
filename: elefunt.bib
label: Taylor:1981:CHD
author: George S. Taylor
title: Compatible hardware for division and square root
crossref: IEEE:1981:PSC
pages: 127--134
year: 1981
bibdate: Mon Sep 16 16:30:51 2002
bibtimestamp: 2002.09.16 16:30:51 ???
URL: http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Taylor.pdf
keywords: ARITH-5
acknowledgement: ack-nhfb
rawauthor: George S. Taylor
rawtitle: Compatible hardware for division and square root
abstract:
Hardware for radix four division and radix two square root is shared in a processor designed to implement the proposed IEEE floating-point standard. The division hardware looks ahead to find the next quotient digit in parallel with the next partial remainder. An 8-bit ALU estimates the next remainder's leading bits. The quotient digit look-up table is addressed with a truncation of the estimate rather than a truncation of the full partial remainder. The estimation ALU and the look-up table are asymmetric for positive and negative remainders. This asymmetry reduces the width of the ALU and the number of minterms in the logic equations for the look-up table. The square root algorithm obtains the correctly rounded result in about two division times using small extensions to the division hardware.

rawabstract:
Hardware for radix four division and radix two square root is shared in a processor designed to implement the proposed IEEE floating-point standard. The division hardware looks ahead to find the next quotient digit in parallel with the next partial remainder. An 8-bit ALU estimates the next remainder's leading bits. The quotient digit look-up table is addressed with a truncation of the estimate rather than a truncation of the full partial remainder. The estimation ALU and the look-up table are asymmetric for positive and negative remainders. This asymmetry reduces the width of the ALU and the number of minterms in the logic equations for the look-up table. The square root algorithm obtains the correctly rounded result in about two division times using small extensions to the division hardware.

entry:
@InProceedings{Taylor:1981:CHD,
  author =       "George S. Taylor",
  title =        "Compatible hardware for division and square root",
  crossref =     "IEEE:1981:PSC",
  pages =        "127--134",
  year =         "1981",
  bibdate =      "Mon Sep 16 16:30:51 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Taylor.pdf",
  abstract =     "Hardware for radix four division and radix two square
                 root is shared in a processor designed to implement the
                 proposed IEEE floating-point standard. The division
                 hardware looks ahead to find the next quotient digit in
                 parallel with the next partial remainder. An 8-bit ALU
                 estimates the next remainder's leading bits. The
                 quotient digit look-up table is addressed with a
                 truncation of the estimate rather than a truncation of
                 the full partial remainder. The estimation ALU and the
                 look-up table are asymmetric for positive and negative
                 remainders. This asymmetry reduces the width of the ALU
                 and the number of minterms in the logic equations for
                 the look-up table. The square root algorithm obtains
                 the correctly rounded result in about two division
                 times using small extensions to the division
                 hardware.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5",
}


bibtype: article
filename: elefunt.bib
label: Temme:1981:ECH
author: N. M. Temme
title: On the expansion of confluent hypergeometric functions in terms of Bessel functions
journal: j-J-COMPUT-APPL-MATH
volume: 7
number: 1
pages: 27--32
month: mar
monthnumber: 3
year: 1981
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 11:59:21 MST 2017
bibtimestamp: 2017.02.25 11:59:21 MST
URL: http://www.sciencedirect.com/science/article/pii/0771050X81900048
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: N. M. Temme
rawtitle: On the expansion of confluent hypergeometric functions in terms of {Bessel} functions
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1980.bib

entry:
@Article{Temme:1981:ECH,
  author =       "N. M. Temme",
  title =        "On the expansion of confluent hypergeometric functions
                 in terms of {Bessel} functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "7",
  number =       "1",
  pages =        "27--32",
  month =        mar,
  year =         "1981",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 11:59:21 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1980.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0771050X81900048",
  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: Terras:1981:ASI
author: Riho Terras
title: Algorithms for some integrals of Bessel functions and multivariate Gaussian integrals
journal: j-J-COMPUT-PHYS
volume: 41
number: 1
pages: 192--199
month: may
monthnumber: 5
year: 1981
CODEN: JCTPAH
DOI: https://doi.org/10.1016/0021-9991(81)90087-5
ISSN: 0021-9991 (print), 1090-2716 (electronic) OR 00219991 (print), 10902716 (electronic)
ISSNL: 0021-9991 OR 00219991
bibdate: Sun Jan 1 15:59:06 MST 2012
bibtimestamp: 2012.01.01 15:59:06 MST
URL: http://www.sciencedirect.com/science/article/pii/0021999181900875
fjournal: Journal of Computational Physics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00219991/
rawauthor: Riho Terras
rawtitle: Algorithms for some integrals of {Bessel} functions and multivariate {Gaussian} integrals
entry:
@Article{Terras:1981:ASI,
  author =       "Riho Terras",
  title =        "Algorithms for some integrals of {Bessel} functions
                 and multivariate {Gaussian} integrals",
  journal =      j-J-COMPUT-PHYS,
  volume =       "41",
  number =       "1",
  pages =        "192--199",
  month =        may,
  year =         "1981",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(81)90087-5",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Sun Jan 1 15:59:06 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1980.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0021999181900875",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}


bibtype: article
filename: elefunt.bib
label: Terras:1981:MAI
author: Riho Terras
title: A Miller algorithm for an incomplete Bessel function
journal: j-J-COMPUT-PHYS
volume: 39
number: 1
pages: 233--240
month: jan
monthnumber: 1
year: 1981
CODEN: JCTPAH
DOI: https://doi.org/10.1016/0021-9991(81)90147-9
ISSN: 0021-9991 (print), 1090-2716 (electronic) OR 00219991 (print), 10902716 (electronic)
ISSNL: 0021-9991 OR 00219991
bibdate: Sun Jan 1 15:59:04 MST 2012
bibtimestamp: 2012.01.01 15:59:04 MST
URL: http://www.sciencedirect.com/science/article/pii/0021999181901479
fjournal: Journal of Computational Physics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00219991/
rawauthor: Riho Terras
rawtitle: A {Miller} algorithm for an incomplete {Bessel} function
entry:
@Article{Terras:1981:MAI,
  author =       "Riho Terras",
  title =        "A {Miller} algorithm for an incomplete {Bessel}
                 function",
  journal =      j-J-COMPUT-PHYS,
  volume =       "39",
  number =       "1",
  pages =        "233--240",
  month =        jan,
  year =         "1981",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(81)90147-9",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Sun Jan 1 15:59:04 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1980.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0021999181901479",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}


bibtype: article
filename: elefunt.bib
label: Vogelius:1981:DRM
author: M. Vogelius and I. Babuska
title: On a dimensional reduction method. II. Some approximation-theoretic results
journal: j-MATH-COMPUT
volume: 37
number: 155
pages: 47--68
month: jul
monthnumber: 7
year: 1981
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Fri Nov 8 18:01:57 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2002.11.08 18:01:57 MST
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: M. Vogelius and I. Babuska
rawtitle: On a dimensional reduction method. {II}. {Some} approximation-theoretic results
subject:
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS

entry:
@Article{Vogelius:1981:DRM,
  author =       "M. Vogelius and I. Babuska",
  title =        "On a dimensional reduction method. {II}. {Some}
                 approximation-theoretic results",
  journal =      j-MATH-COMPUT,
  volume =       "37",
  number =       "155",
  pages =        "47--68",
  month =        jul,
  year =         "1981",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  catcode =      "G.1.2; G.1.7",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation; G.1.7 Ordinary Differential Equations;
                 G.1.7 Boundary value problems",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary
                 Differential Equations, Boundary value problems",
  fjournal =     "Mathematics of Computation",
  genterm =      "theory",
  guideno =      "09396",
  journal-URL =  "http://www.ams.org/mcom/",
  jrldate =      "July 1981",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}


bibtype: book
filename: elefunt.bib
label: Wimp:1981:STT
author: Jet Wimp
title: Sequence Transformations and Their Applications
volume: 154
publisher: pub-ACADEMIC
address: pub-ACADEMIC:adr
pages: xix + 257
year: 1981
ISBN: 0-08-095662-9 (e-book), 0-12-757940-0 OR 0080956629 (ebook), 0127579400
ISBN13: 978-0-08-095662-6 (e-book), 978-0-12-757940-5 OR 9780080956626 (ebook), 9780127579405
LCCN: QA292 .W54
bibdate: Thu Dec 1 11:08:47 MST 2011
bibsource: fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2011.12.01 11:08:47 MST
series: Mathematics in Science and Engineering
URL: http://public.eblib.com/EBLPublic/PublicView.do?ptiID=453177
acknowledgement: ack-nhfb
rawauthor: Jet Wimp
rawtitle: Sequence Transformations and Their Applications
subject:
Sequences (Mathematics) Transformations (Mathematics) Numerical analysis; Acceleration of convergence

TOC:
Front Cover Sequence Transformations and Their Applications Copyright Page Contents Preface Acknowledgments Notation Chapter 1. Sequences and Series Chapter 2. Linear Transformations Chapter 3. Linear Lozenge Methods Chapter 4. Optimal Methods and Methods Based on Power Series Chapter 5. Nonlinear Lozenges Iteration Sequences Chapter 6. The Schmidt Transformation The e-Algorithm Chapter 7. Aitken's $d^2$-Process and Related Methods Chapter 8. Lozenge Algorithms and the Theory of Continued Fractions Chapter 9. Other Lozenge Algorithms and Nonlinear MethodsChapter 10. The Brezinski--Haa vie ProtocolChapter 11. The Brezinski--Haa vie Protocol and Numerical Quadrature Chapter 12. Probabilistic Methods Chapter 13. Multiple Sequences Appendix Bibliography Index

rawTOC:
Front Cover \\ Sequence Transformations and Their Applications \\ Copyright Page \\ Contents \\ Preface \\ Acknowledgments \\ Notation \\ Chapter 1. Sequences and Series \\ Chapter 2. Linear Transformations \\ Chapter 3. Linear Lozenge Methods \\ Chapter 4. Optimal Methods and Methods Based on Power Series \\ Chapter 5. Nonlinear Lozenges \\ Iteration Sequences \\ Chapter 6. The Schmidt Transformation \\ The e-Algorithm \\ Chapter 7. Aitken's $d^2$-Process and Related Methods \\ Chapter 8. Lozenge Algorithms and the Theory of Continued Fractions \\ Chapter 9. Other Lozenge Algorithms and Nonlinear MethodsChapter 10. The Brezinski--H{\aa}vie ProtocolChapter 11. The Brezinski--H{\aa}vie Protocol and Numerical Quadrature \\ Chapter 12. Probabilistic Methods \\ Chapter 13. Multiple Sequences \\ Appendix \\ Bibliography \\ Index

entry:
@Book{Wimp:1981:STT,
  author =       "Jet Wimp",
  title =        "Sequence Transformations and Their Applications",
  volume =       "154",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "xix + 257",
  year =         "1981",
  ISBN =         "0-08-095662-9 (e-book), 0-12-757940-0",
  ISBN-13 =      "978-0-08-095662-6 (e-book), 978-0-12-757940-5",
  LCCN =         "QA292 .W54",
  bibdate =      "Thu Dec 1 11:08:47 MST 2011",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Mathematics in Science and Engineering",
  URL =          "http://public.eblib.com/EBLPublic/PublicView.do?ptiID=453177",
  acknowledgement = ack-nhfb,
  subject =      "Sequences (Mathematics) Transformations (Mathematics)
                 Numerical analysis; Acceleration of convergence",
  tableofcontents = "Front Cover \\
                 Sequence Transformations and Their Applications \\
                 Copyright Page \\
                 Contents \\
                 Preface \\
                 Acknowledgments \\
                 Notation \\
                 Chapter 1. Sequences and Series \\
                 Chapter 2. Linear Transformations \\
                 Chapter 3. Linear Lozenge Methods \\
                 Chapter 4. Optimal Methods and Methods Based on Power
                 Series \\
                 Chapter 5. Nonlinear Lozenges \\
                 Iteration Sequences \\
                 Chapter 6. The Schmidt Transformation \\
                 The e-Algorithm \\
                 Chapter 7. Aitken's $d^2$-Process and Related Methods
                 \\
                 Chapter 8. Lozenge Algorithms and the Theory of
                 Continued Fractions \\
                 Chapter 9. Other Lozenge Algorithms and Nonlinear
                 MethodsChapter 10. The Brezinski--H{\aa}vie
                 ProtocolChapter 11. The Brezinski--H{\aa}vie Protocol
                 and Numerical Quadrature \\
                 Chapter 12. Probabilistic Methods \\
                 Chapter 13. Multiple Sequences \\
                 Appendix \\
                 Bibliography \\
                 Index",
}


bibtype: article
filename: elefunt.bib
label: Andrews:1982:MMS
author: M. Andrews
title: Mathematical Microprocessor Software: a $ sqrt (x) $ Comparison
journal: j-IEEE-MICRO
volume: 2
number: 3
pages: 63--79
month: may
monthnumber: 5
year: 1982
CODEN: IEMIDZ
DOI: https://doi.org/10.1109/MM.1982.290970
ISSN: 0272-1732 (print), 1937-4143 (electronic) OR 02721732 (print), 19374143 (electronic)
ISSNL: 0272-1732 OR 02721732
bibdate: Thu Dec 14 06:08:58 MST 2000
bibtimestamp: 2000.12.14 06:08:58 MST
fjournal: IEEE Micro
acknowledgement: ack-nj
corpsource: Colorado State Univ., Fort Collins, CO, USA
journalURL: http://www.computer.org/csdl/mags/mi/index.html
treatment: T Theoretical or Mathematical
rawauthor: M. Andrews
rawtitle: Mathematical Microprocessor Software: a $ \sqrt (x) $ Comparison
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt; 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/ieeemicro.bib; Science Citation Index database (1980--2000)

keywords:
16-bit machines; 8-bit machine; accuracy; Chen method; computer testing; Cordic method; direct method; function approximation; hardware; Intel 8080; Newton method; PDP-11/20; software requirements; speed; square-roots

classcodes:
C4130 (Interpolation and function approximation); C6150G (Diagnostic, testing, debugging and evaluating systems)

entry:
@Article{Andrews:1982:MMS,
  author =       "M. Andrews",
  title =        "Mathematical Microprocessor Software: a $ \sqrt (x) $
                 Comparison",
  journal =      j-IEEE-MICRO,
  volume =       "2",
  number =       "3",
  pages =        "63--79",
  month =        may # "\slash " # jun,
  year =         "1982",
  CODEN =        "IEMIDZ",
  DOI =          "https://doi.org/10.1109/MM.1982.290970",
  ISSN =         "0272-1732 (print), 1937-4143 (electronic)",
  ISSN-L =       "0272-1732",
  bibdate =      "Thu Dec 14 06:08:58 MST 2000",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 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/ieeemicro.bib;
                 Science Citation Index database (1980--2000)",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  classcodes =   "C4130 (Interpolation and function approximation);
                 C6150G (Diagnostic, testing, debugging and evaluating
                 systems)",
  corpsource =   "Colorado State Univ., Fort Collins, CO, USA",
  fjournal =     "IEEE Micro",
  journal-URL =  "http://www.computer.org/csdl/mags/mi/index.html",
  keywords =     "16-bit machines; 8-bit machine; accuracy; Chen method;
                 computer testing; Cordic method; direct method;
                 function approximation; hardware; Intel 8080; Newton
                 method; PDP-11/20; software requirements; speed;
                 square-roots",
  treatment =    "T Theoretical or Mathematical",
}


