Last update:
Tue Mar 20 16:20:05 MDT 2007
Preston C. Hammer and
Howard H. Wicke Quadrature Formulas Involving
Derivatives of the Integrand . . . . . . 3--7
George Struble Tables for Use in Quadrature Formulas
Involving Derivatives of the Integrand 8--12
J. C. P. Miller Numerical Quadrature Over a Rectangular
Domain in Two or More Dimensions: Part
1. Quadrature over a Square, Using up to
Sixteen Equally Spaced Points . . . . . 13--20
A. H. Stroud Numerical Integration Formulas of Degree
Two . . . . . . . . . . . . . . . . . . 21--26
Thomas S. Walton and
Harry Polachek Calculation of Transient Motion of
Submerged Cables . . . . . . . . . . . . 27--46
Philip Rabinowitz Abscissas and Weights for Lobatto
Quadrature of High Order . . . . . . . . 47--52
I. M. Longman A Method for the Numerical Evaluation of
Finite Integrals of Oscillatory
Functions . . . . . . . . . . . . . . . 53--59
Joseph Gillis and
George Weiss Products of Laguerre Polynomials . . . . 60--63
F. L. Bauer The Formula-Controlled Logical Computer
``Stanislaus'' (in Technical Notes and
Short Papers) . . . . . . . . . . . . . 64--67
Chih-Bing Ling Evaluation at Half Periods of
Weierstrass' Elliptic Function With
Rectangular Primitive
Period-Parallelogram . . . . . . . . . . 67--70
Raymond B. Killgrove A Note on the Nonexistence of Certain
Projective Planes of Order Nine . . . . 70--71
Robert W. Floyd A Note on Rational Approximation . . . . 72--73
K. R. Isemanger The Complete Factorization of $2^{132} +
1$ . . . . . . . . . . . . . . . . . . . 73--74
Anonymous Corrigenda . . . . . . . . . . . . . . . 97--97
J. D. Swift Construction of Galois Fields of
Characteristic Two and Irreducible
Polynomials . . . . . . . . . . . . . . 99--103
Stig Comet Improved Methods to Calculate the
Characters of the Symmetric Group . . . 104--117
E. T. Kirkpatrick Tables of Values of the Modified Mathieu
Functions . . . . . . . . . . . . . . . 118--129
J. C. P. Miller Numerical Quadrature over a Rectangular
Domain in Two or More Dimensions . . . . 130--138
Arnold N. Lowan On the Propagation of Round-Off Errors
in the Numerical Integration of the Heat
Equation . . . . . . . . . . . . . . . . 139--146
P. Wynn The Rational Approximation of Functions
which are Formally Defined by a Power
Series Expansion . . . . . . . . . . . . 147--186
I. M. Longman On the Utility of Newton's Method for
Computing Complex Roots of Equations (in
Technical Notes and Short Papers) . . . 187--189
Gordon Pall and
Esther Seiden A Problem in Abelian Groups, with
Application to the Transposition of a
Matrix on an Electronic Computer (in
Technical Notes and Short Papers) . . . 189--192
Charles Walmsley and
Arthur S. G. Grant The Fourier Transform of $\lbrack c^{2k}
+ (x - x^{-1})^{2k} \rbrack^{-1}$
Arising from Study of Tuned Circuit
Spectra (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 193--195
H. A. Lang On the Evaluation of Certain Complex
Elliptic Integrals (in Technical Notes
and Short Papers) . . . . . . . . . . . 195--199
D. Scheffler and
R. Ondrejka The Numerical Evaluation of the
Eighteenth Perfect Number (in Technical
Notes and Short Papers) . . . . . . . . 199--200
Daniel Shanks A Note on Gaussian Twin Primes (in
Technical Notes and Short Papers) . . . 201--203
Anonymous Corrigenda . . . . . . . . . . . . . . . 222--222
Arnold N. Lowan On the Propagation of Round-Off Errors
in the Numerical Treatment of the Wave
Equation . . . . . . . . . . . . . . . . 223--228
Michael Goldberg Rotors in Polygons and Polyhedra . . . . 229--239
J. C. P. Miller Numerical Quadrature Over a Rectangular
Domain in Two or More Dimensions. Part
3: Quadrature of a Harmonic Integrand 240--248
Milton E. Rose A Method for Calculating Solutions of
Parabolic Equations with a Free Boundary 249--256
Herbert E. Salzer Alternative Formulas for Osculatory and
Hyperosculatory Inverse Interpolation 257--261
Paul J. Nikolai Permanents of Incidence Matrices (in
Technical Notes and Short Papers) . . . 262--266
Arnold N. Lowan On the Numerical Treatment of Heat
Conduction Problems with Mixed Boundary
Conditions (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 266--270
I. E. Perlin and
J. R. Garrett High Precision Calculation of
$\operatorname{Arcsin} x$,
$\operatorname{Arccos} x$, and
$\operatorname{Arctan} x$ (in Technical
Notes and Short Papers) . . . . . . . . 270--274
A. Rotenberg The Calculation of Toroidal Harmonics
(in Technical Notes and Short Papers) 274--276
J. R. M. Radok Transcendental Equation for the
Schrödinger Equation (in Technical Notes
and Short Papers) . . . . . . . . . . . 276--278
A. Gloden A Note on Factors of $n^4 + 1$ (in
Technical Notes and Short Papers) . . . 278--279
Herbert E. Salzer A Note on the Solution of Quartic
Equations (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 279--281
D. A. Magula A Conjugate Factor Method for the
Solution of a Cubic (in Technical Notes
and Short Papers) . . . . . . . . . . . 281--283
Anonymous Corrigendum . . . . . . . . . . . . . . 310--310
R. Sherman Lehman On Liouville's Function . . . . . . . . 311--320
Daniel Shanks On the Conjecture of Hardy & Littlewood
concerning the ``Number of Primes of the
Form $n^2 + a$'' . . . . . . . . . . . . 321--332
Arnold N. Lowan On the Propagation of Errors in the
Inversion of Certain Tridiagonal
Matrices . . . . . . . . . . . . . . . . 333--338
Daniel C. Fielder Tabulation of Coefficients for
Operations on Taylor Series . . . . . . 339--345
Marcia Ascher Explicit Solutions of the
One-Dimensional Heat Equation for a
Composite Wall . . . . . . . . . . . . . 346--353
David A. Pope A Method of ``Alternating Corrections''
for the Numerical Solution of Two-Point
Boundary Value Problems . . . . . . . . 354--361
E. Dempsey and
G. C. Benson Note on the Asymptotic Expansion of the
Modified Bessel Function of the Second
Kind (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 362--365
John Brillhart and
G. D. Johnson On the Factors of Certain Mersenne
Numbers (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 365--369
John W. Wrench, Jr. Further Evaluation of Khintchine's
Constant (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 370--371
H. E. Fettis Note on $\int\sp \infty\sb 0 e\sp{-x}
{J}\sb 0 \left(\frac{\eta
x}{\epsilon}\right) {J}\sb
1\left(\frac{x}{\epsilon}\right)
x\sp{-n} dx$ . . . . . . . . . . . . . . 372--374
Henry E. Fettis Note on $\int^\infty_0 e^{-x}{J}_0
\Big(\frac{\eta x}{\xi}\Big) {J}_1
\Big(\frac{x}{\xi}\Big) x^{-n} dx$ (in
Technical Notes and Short Papers) . . . 372--374
R. D. Lord Integrals of Products of Laguerre
Polynomials (in Technical Notes and
Short Papers) . . . . . . . . . . . . . 375--376
Irwin Greenberg The Evaluation of Certain Probability
Integrals (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 376--378
Sidney Kravitz The Congruence $2^{p-1} \equiv 1
(\operatorname{mod} p^2) \text{for} p <
100,000$ (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 378--378
Kasaburo Harumi and
Shigetoshi Katsura and
John W. Wrench, Jr. Values of $\frac{2}{\pi} \int^\infty_0
\Big(\frac{\sin t}{t}\Big)^n dt$ (in
Technical Notes and Short Papers) . . . 379--379
J. Boersma Computation of Fresnel Integrals (in
Technical Notes and Short Papers) . . . 380--380
George Shortley Book Review: \em The $3$-j and $6$-j
Symbols, by Manuel Rotenberg, R. Bivins,
N. Metropolis, and John K. Wooten, Jr. 382--383
O. Shisha The Chebyshev polynomial of best
approximation to a given function on an
interval . . . . . . . . . . . . . . . . 266--271
Murlan S. Corrington Applications of the Complex Exponential
Integral . . . . . . . . . . . . . . . . 1--6
Richard Barakat Evaluation of the Incomplete Gamma
Function of Imaginary Argument by
Chebyshev Polynomials . . . . . . . . . 7--11
C. W. Nelson New Tables of Howland's and Related
Integrals . . . . . . . . . . . . . . . 12--18
Gilbert C. Best Two Theorem Tables of Matrix Algebra . . 19--22
Herbert E. Salzer and
Genevieve M. Kimbro Improved Formulas for Complete and
Partial Summation of Certain Series . . 23--39
Henry Stone Approximation of Curves by Line Segments 40--47
F. C. Ledsham Numerical Integration Using Sums of
Exponential Functions (in Technical
Notes and Short Papers) . . . . . . . . 48--51
Edgar Karst New Factors of Mersenne Numbers (in
Technical Notes and Short Papers) . . . 51--51
A. H. Stroud A Bibliography on Approximate
Integration (in Surveys and Expository
Papers) . . . . . . . . . . . . . . . . 52--80
Anonymous Corrigenda . . . . . . . . . . . . . . . 113--114
William J. Kammerer Polynomial Approximations to Finitely
Oscillating Functions . . . . . . . . . 115--119
Herbert E. Salzer and
Norman Levine Table of a Weierstrass Continuous
Non-Differentiable Function . . . . . . 120--130
J. G. Jones On the Numerical Solution of Convolution
Integral Equations and Systems of Such
Equations . . . . . . . . . . . . . . . 131--142
A. H. Stroud Numerical Integration Formulas of Degree
$3$ for Product Regions and Cones . . . 143--150
P. Wynn The Epsilon Algorithm and Operational
Formulas of Numerical Analysis . . . . . 151--158
A. M. Arthurs and
R. McCarroll Expansion of Spherical Bessel Functions
in a Series of Chebyshev Polynomials . . 159--162
Harry A. Rothmann Gaussian Quadrature with Weight Function
$x^n$ on the Interval $(-1, 1)$ . . . . 163--168
Harry Weingarten and
A. R. Di Donato A Table of Generalized Circular Error 169--173
Jet Wimp Polynomial Approximations to Integral
Transforms . . . . . . . . . . . . . . . 174--178
Arnold N. Lowan On Stability Criteria of Explicit
Difference Schemes for Certain Heat
Conduction Problems with Uncommon
Boundary Conditions . . . . . . . . . . 179--185
Daniel Shanks On Numbers of the Form $n^4 + 1$ . . . . 186--189
Henry B. Mann On Modular Computation (in Technical
Notes and Short Papers) . . . . . . . . 190--192
Mark B. Wells Generation of Permutations by
Transposition (in Technical Notes and
Short Papers) . . . . . . . . . . . . . 192--195
Helmut Werner and
Robert Collinge Chebyshev Approximations to the Gamma
Function (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 195--197
J. C. Butcher A Partition Test for Pseudo-Random
Numbers (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 198--199
Anonymous Corrigenda . . . . . . . . . . . . . . . 225--225
Walter Gautschi Recursive Computation of the Repeated
Integrals of the Error Function . . . . 227--232
Yudell L. Luke and
Richard L. Coleman Expansion of Hypergeometric Functions in
Series of Other Hypergeometric Functions 233--237
A. R. Mitchell Solution of the von Mises Boundary Layer
Equation Using a High-Speed Computer . . 238--242
M. M. Pennell and
L. M. Delves The Numerical Solution of Coupled
Integro-Differential Equations . . . . . 243--249
Hidehiko Yamabe and
David Pope A Computational Approach to the
Four-Color Problem . . . . . . . . . . . 250--253
Jack Levine Some Applications of High-Speed
Computers to the Case $n = 2$ of
Algebraic Cryptography . . . . . . . . . 254--260
L. Filler and
H. F. Ludloff Stability Analysis and Integration of
the Viscous Equations of Motion . . . . 261--274
A. Lazarkiewicz and
W. Balasinski A Simple Experimental Computer with
Negative Basis . . . . . . . . . . . . . 275--285
Stephen M. Robinson and
A. H. Stroud The Approximate Solution of an Integral
Equation Using High-Order Gaussian
Quadrature Formulas (in Technical Notes
and Short Papers) . . . . . . . . . . . 286--288
Ferdinand Freudenstein Bi-Variate, Rectangular,
Optimum-Interval Interpolation (in
Technical Notes and Short Papers) . . . 288--291
Sidney Kravitz Divisors of Mersenne Numbers $10,000 < p <
15,000$ (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 292--293
R. T. Ostrowski and
K. D. Van Duren On a Theorem of Mann on Latin Squares
(in Technical Notes and Short Papers) 293--295
K. R. Isemonger Complete Factorization of $2^{159} - 1$
(in Technical Notes and Short Papers) 295--296
J. Boersma Two Formulas Relating to Elliptic
Integrals of the Third Kind (in
Technical Notes and Short Papers) . . . 296--298
C. B. Haselgrove A Method for Numerical Integration . . . 323--337
Feodor Theilheimer and
William Starkweather The Fairing of Ship Lines on a
High-Speed Computer . . . . . . . . . . 338--355
G. J. Habetler and
E. L. Wachspress Symmetric Successive Overrelaxation In
Solving Diffusion Difference Equations 356--362
J. W. Cooley An Improved Eigenvalue Corrector Formula
for Solving the Schrödinger Equation for
Central Fields . . . . . . . . . . . . . 363--374
A. R. DiDonato and
M. P. Jarnagin Integration of the General Bivariate
Gaussian Distribution over an Offset
Circle . . . . . . . . . . . . . . . . . 375--382
Martin Greenberger An A Priori Determination of Serial
Correlation in Computer Generated Random
Numbers . . . . . . . . . . . . . . . . 383--389
Jerry L. Fields and
Jet Wimp Expansions of Hypergeometric Functions
in Hypergeometric Functions . . . . . . 390--395
John W. Wrench, Jr. Evaluation of Artin's Constant and the
Twin-Prime Constant . . . . . . . . . . 396--398
Henry C. Thacher, Jr. Iterated Square Root Expansions for the
Inverse Cosine and Inverse Hyperbolic
Cosine . . . . . . . . . . . . . . . . . 399--403
J. S. Dranoff An Eigenvalue Problem Arising In Mass
and Heat Transfer Studies . . . . . . . 403--409
Kurt Spielberg Efficient Continued Fraction
Approximations To Elementary Functions 409--417
N. Ream Note on ``Approximation of Curves by
Line Segments'' . . . . . . . . . . . . 418--419
G. A. Paxson The Compositeness of the Thirteenth
Fermat Number . . . . . . . . . . . . . 420--420
Anonymous Corrigenda . . . . . . . . . . . . . . . 436--436
J. Kampe de Feriet and
François N. Frenkiel Correlations and Spectra for
Non-Stationary Random Functions . . . . 1--21
Arnold Nordsieck On Numerical Integration of Ordinary
Differential Equations . . . . . . . . . 22--49
J. Gillis and
M. Shimshoni Triple Product Integrals of Laguerre
Functions . . . . . . . . . . . . . . . 50--62
V. D. Barnett The Behavior of Pseudo-Random Sequences
Generated on Computers by the
Multiplicative Congruential Method . . . 63--69
Milton Lees A Note on the Convergence of Alternating
Direction Methods . . . . . . . . . . . 70--75
Daniel Shanks and
John W. Wrench, Jr. Calculation of $\pi$ to 100,000 Decimals 76--99
T. Tamir Characteristic Exponents of Mathieu
Functions (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 100--106
Robert D. Stalley An Algorithm for Solving Certain
Polynomial Equations with Coefficient
Parameters (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 106--109
Bernard Epstein A Remark Concerning the Solution of the
Dirichlet Problem by Finite Differences
(in Technical Notes and Short Papers) 110--112
Anonymous Corrigenda . . . . . . . . . . . . . . . 126--126
Harvey Cohn A Numerical Study of the Relative Class
Numbers of Real Quadratic Integral
Domains . . . . . . . . . . . . . . . . 127--140
D. G. Cantor and
G. Estrin and
A. S. Fraenkel and
R. Turn A Very High-Speed Digital Number Sieve 141--154
R. P. Pearce and
A. R. Mitchell On Finite Difference Methods of Solution
of the Transport Equation . . . . . . . 155--169
W. M. Harper Quadrature Formulas for Infinite
Integrals . . . . . . . . . . . . . . . 170--175
E. K. Blum A Modification of the Runge--Kutta
Fourth-Order Method . . . . . . . . . . 176--187
R. K. Pathria A Statistical Study of Randomness Among
the First $10,000$ Digits of $\pi$ . . . 188--197
John F. Bridge and
Stanley W. Angrist An Extended Table of Roots of ${J}_n'(x)
{Y}_n'(\beta x) - {J}_n'(\beta x)
{Y}_n'(x) = 0$ . . . . . . . . . . . . . 198--204
Kurt Spielberg Polynomial and Continued-Fraction
Approximations for Logarithmic Functions 205--217
H. S. Shapiro Some Remarks on Modular Arithmetic and
Parallel Computation (in Technical Notes
and Short Papers) . . . . . . . . . . . 218--222
Frank Harary Permutations with Restricted Position
(in Technical Notes and Short Papers) 222--226
L. Jackson Laslett and
William Lewish Evaluation of the Zeros of Cross-Product
Bessel Functions (in Technical Notes and
Short Papers) . . . . . . . . . . . . . 226--232
J. Boersma On the Computation of Lommel's Functions
of Two Variables (in Technical Notes and
Short Papers) . . . . . . . . . . . . . 232--238
A. Gloden Additions to Cunningham's Factor Table
of $n^4 + 1$ (in Technical Notes and
Short Papers) . . . . . . . . . . . . . 239--241
Gary Lotto On the Generation of All Possible
Stepwise Combinations (in Technical
Notes and Short Papers) . . . . . . . . 241--243
John R. Howell Generation of Permutations by Addition
(in Technical Notes and Short Papers) 243--244
Herbert E. Salzer Multiple Quadrature with Central
Differences on One Line (in Technical
Notes and Short Papers) . . . . . . . . 244--248
Alexander Hurwitz New Mersenne Primes (in Technical Notes
and Short Papers) . . . . . . . . . . . 249--251
Anonymous Corrigenda . . . . . . . . . . . . . . . 262--263
Eldon R. Hansen and
Merrell L. Patrick Some Relations and Values for the
Generalized Riemann Zeta Function . . . 265--274
Donald E. Knuth Euler's Constant to $1271$ Places . . . 275--281
W. Fraser and
C. C. Gotlieb A Calculation of the Number of Lattice
Points in the Circle and Sphere . . . . 282--290
K. M. Brown and
P. Henrici Sign Wave Analysis in Matrix Eigenvalue
Problems . . . . . . . . . . . . . . . . 291--300
P. Wynn Acceleration Techniques for Iterated
Vector and Matrix Problems . . . . . . . 301--322
J. Schröder Computing Error Bounds in Solving Linear
Systems . . . . . . . . . . . . . . . . 323--337
M. R. Osborne A Note on Finite Difference Methods for
Solving the Eigenvalue Problems of
Second-Order Differential Equations . . 338--346
A. R. DiDonato and
M. P. Jarnagin A Method for Computing the Circular
Coverage Function . . . . . . . . . . . 347--355
Herbert E. Salzer Optimum-Point Formulas for Osculatory
and Hyperosculatory Interpolation . . . 356--362
Paul T. Bateman and
Roger A. Horn A Heuristic Asymptotic Formula
Concerning the Distribution of Prime
Numbers (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 363--367
E. J. Watson Primitive polynomials (mod $2$) . . . . 368--369
E. J. Watson Primitive Polynomials
$(\operatorname{Mod} 2)$ (in Technical
Notes and Short Papers) . . . . . . . . 368--369
H. H. Denman and
R. C. W. Ettinger Note on Latent Roots and Vectors of
Segments of the Hilbert Matrix (in
Technical Notes and Short Papers) . . . 370--371
Y. K. Lin and
F. A. Lee Expansions of Jacobian Elliptic
Functions in Powers of the Modulus (in
Technical Notes and Short Papers) . . . 372--375
Anonymous Corrigendum . . . . . . . . . . . . . . 406--406
D. H. Lehmer and
E. Lehmer and
W. H. Mills and
J. L. Selfridge Machine Proof of a Theorem on Cubic
Residues . . . . . . . . . . . . . . . . 407--415
Jack Levine and
R. E. Dalton Minimum Periods, Modulo $p$, of
First-Order Bell Exponential Integers 416--423
John Brillhart Concerning the Numbers $2^{2p} + 1, p$
Prime . . . . . . . . . . . . . . . . . 424--430
Anthony Ralston Runge--Kutta Methods with Minimum Error
Bounds . . . . . . . . . . . . . . . . . 431--437
Gene H. Golub Bounds for Eigenvalues of Tridiagonal
Symmetric Matrices Computed by the LR
Method . . . . . . . . . . . . . . . . . 438--445
Jet Wimp Polynomial Expansions of Bessel
Functions and Some Associated Functions 446--458
S. Muroga and
I. Toda and
M. Kondo Majority Decision Functions of up to Six
Variables . . . . . . . . . . . . . . . 459--472
R. Bellman and
B. Kotkin On the Numerical Solution of a
Differential-Difference Equation Arising
in Analytic Number Theory (in Technical
Notes and Short Papers) . . . . . . . . 473--475
L. Carlitz The Coefficients of the Lemniscate
Function (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 475--478
H. Riesel All Factors $q < 10^8$ in All Mersenne
Numbers $2^p - 1, p \text{Prime} < 10^4$
(in Technical Notes and Short Papers) 478--482
M. Wunderlich Certain Properties of Pyramidal and
Figurate Numbers (in Technical Notes and
Short Papers) . . . . . . . . . . . . . 482--486
Herbert E. Salzer Note on Osculatory Rational
Interpolation (in Technical Notes and
Short Papers) . . . . . . . . . . . . . 486--491
Charlotte Froese On Solving $y'' = fy + g$ with a
Boundary Condition at Infinity (in
Technical Notes and Short Papers) . . . 492--494
A. L. Dulmage and
N. S. Mendelsohn On the Inversion of Sparse Matrices (in
Technical Notes and Short Papers) . . . 494--496
R. I. Jennrich Missing Data Correlation Computations
(in Technical Notes and Short Papers) 496--497
F. D. Burgoyne Polynomial Approximations to ${I}_0(x),
{I}_1(x)$ and Related Functions (in
Technical Notes and Short Papers) . . . 497--498
F. D. Burgoyne A Note on the Curve Fitting of Discrete
Data by Economization (in Technical
Notes and Short Papers) . . . . . . . . 498--499
Anonymous Corrigendum . . . . . . . . . . . . . . 513--513
W. V. Petryshyn On a General Iterative Method for the
Approximate Solution of Linear Operator
Equations . . . . . . . . . . . . . . . 1--10
John R. B. Whittlesey Incomplete Gamma Functions for
Evaluating Erlang Process Probabilities 11--17
J. Descloux Note on the Round-Off Errors in
Iterative Processes . . . . . . . . . . 18--27
Joel N. Franklin Deterministic Simulation of Random
Processes . . . . . . . . . . . . . . . 28--59
H. Polachek and
T. S. Walton and
R. Mejia and
C. Dawson Transient Motion of an Elastic Cable
Immersed in a Fluid . . . . . . . . . . 60--63
J. N. Newman and
W. Frank An Integral Containing the Square of a
Bessel Function . . . . . . . . . . . . 64--70
Jim Douglas, Jr. and
James E. Gunn Two High-Order Correct Difference
Analogues for the Equation of
Multidimensional Heat Flow . . . . . . . 71--80
T. A. Porsching Matrix Assignments and an Associated Min
Max Problem (in Technical Notes and
Short Papers) . . . . . . . . . . . . . 81--84
James Miller Formulas for Integrals of Products of
Associated Legendre or Laguerre
Functions (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 84--87
Anonymous Corrigenda . . . . . . . . . . . . . . . 104--104
A. H. Stroud and
Don Secrest Approximate Integration Formulas for
Certain Spherically Symmetric Regions 105--135
Daniel Shanks and
John W. Wrench, Jr. The Calculation of Certain Dirichlet
Series . . . . . . . . . . . . . . . . . 136--154
Richard Bellman and
Robert Kalaba and
Bella Kotkin Polynomial Approximation--A New
Computational Technique in Dynamic
Programming: Allocation Processes . . . 155--161
Thomas Erber and
Alan Gordon Tabulation of the Functions
$\frac{\partial I_\nu(z)}{\partial \nu},
\nu = \pm \frac{1}{3}$ . . . . . . . . . 162--169
Dura W. Sweeney On the Computation of Euler's Constant 170--178
David C. Mapes Fast Method for Computing the Number of
Primes Less than a Given Limit . . . . . 179--185
Gene H. Golub On a Lower Bound for the Rank of a
Partitioned Square Matrix . . . . . . . 186--188
Daniel Shanks Supplementary Data and Remarks
Concerning a Hardy--Littlewood
Conjecture . . . . . . . . . . . . . . . 188--193
H. Werner and
G. Raymann An Approximation to the Fermi Integral
${F}_{1/2}(x)$ . . . . . . . . . . . . . 193--194
Erna H. Pearson On the Congruences $(p - 1)! \equiv - 1$
and $2^{p-1} \equiv (\operatorname{mod}
p^2)$ . . . . . . . . . . . . . . . . . 194--195
F. D. Burgoyne The Non-Existence of Certain
Laguerre--Chebyshev Quadrature Formulas 196--197
Donald W. Grace Search for Largest Polyhedra . . . . . . 197--199
Herbert S. Wilf Calculations Relating to a Conjecture of
Polya and Schoenberg . . . . . . . . . . 200--201
Anonymous Corrigenda . . . . . . . . . . . . . . . 215--215
James H. Bramble Fourth-Order Finite Difference Analogues
of the Dirichlet Problem for Poisson's
Equation in Three and Four Dimensions 217--222
H. B. Keller and
J. R. Swenson Experiments on the Lattice Problem of
Gauss . . . . . . . . . . . . . . . . . 223--230
R. W. Preisendorfer and
B. W. Roos On the Best Fit to Experimental Data
Curves Using Homogeneous Two-Parameter
Functions . . . . . . . . . . . . . . . 231--236
H. H. Michels Abscissas and Weight Coefficients for
Lobatto Quadrature . . . . . . . . . . . 237--244
P. Concus and
D. Cassatt and
G. Jaehnig and
E. Melby Tables for the Evaluation of
$\int^\infty_0 x^\beta e^{-x}f(x) dx$ by
Gauss--Laguerre Quadrature . . . . . . . 245--256
F. Ginsberg On the Cauchy Problem for the
One-Dimensional Heat Equation . . . . . 257--269
D. D. Stancu Evaluation of the Remainder Term in
Approximation Formulas by Bernstein
Polynomials . . . . . . . . . . . . . . 270--278
J. Douglas, Jr. and
R. B. Kellogg and
R. S. Varga Alternating Direction Iteration Methods
for $n$ Space Variables (in Technical
Notes and Short Papers) . . . . . . . . 279--282
Selmer M. Johnson Generation of Permutations by Adjacent
Transposition (in Technical Notes and
Short Papers) . . . . . . . . . . . . . 282--285
R. W. Preisendorfer and
B. W. Roos and
W. C. Sangren Determinants by Means of Solutions of
Linear Equations (in Technical Notes and
Short Papers) . . . . . . . . . . . . . 285--289
A. H. Stroud Coefficients in Quadrature Formulas (in
Technical Notes and Short Papers) . . . 289--291
M. H. McAndrew A Partition Problem (in Technical Notes
and Short Papers) . . . . . . . . . . . 291--295
F. D. Burgoyne Approximations to Kelvin Functions (in
Technical Notes and Short Papers) . . . 295--298
F. D. Burgoyne Quadrature Formulas over Infinite
Intervals in Terms of Differences (in
Technical Notes and Short Papers) . . . 298--301
Anonymous Corrigenda . . . . . . . . . . . . . . . 335--335
Israel Navot The Euler--Maclaurin Functional for
Functions with a Quasi-Step
Discontinuity . . . . . . . . . . . . . 337--345
Bart J. Daly The Stability Properties of a Coupled
Pair of Non-Linear Partial Difference
Equations . . . . . . . . . . . . . . . 346--360
A. D. McLaren Optimal Numerical Integration on a
Sphere . . . . . . . . . . . . . . . . . 361--383
D. D. Stancu and
A. H. Stroud Quadrature Formulas with Simple Gaussian
Nodes and Multiple Fixed Nodes . . . . . 384--394
Y. L. Luke and
J. Wimp Jacobi Polynomial Expansions of a
Generalized Hypergeometric Function over
a Semi-Infinite Ray . . . . . . . . . . 395--404
George W. Batten, Jr. Second-Order Correct Boundary Conditions
for the Numerical Solution of the Mixed
Boundary Problem for Parabolic Equations 405--413
R. Sankar and
V. Malini A Note on the Relative Merits of Padé and
Maehly's Diagonal Convergents in
Computing $e^x$ . . . . . . . . . . . . 414--418
R. E. von Holdt and
R. J. Howerton The Definite Integral of the Product of
Linear Functions . . . . . . . . . . . . 419--425
A. R. Mitchell and
R. P. Pearce Explicit Difference Methods for Solving
the Cylindrical Heat Conduction Equation 426--432
C. Donald La Budde The Reduction of an Arbitrary Real
Square Matrix to Tri-Diagonal Form Using
Similarity Transformations (in Technical
Notes and Short Papers) . . . . . . . . 433--437
J. T. Day A Gaussian Quadrature Method for the
Numerical Solution of the Characteristic
Initial Value Problem $u_{xy} = f(x, y,
u)$ (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 438--441
George Shapiro Gauss Elimination for Singular Matrices
(in Technical Notes and Short Papers) 441--445
A. Schinzel A Remark on a Paper of Bateman and Horn
(in Technical Notes and Short Papers) 445--447
John Brillhart Some Miscellaneous Factorizations (in
Technical Notes and Short Papers) . . . 447--450
S. R. Cavior A Note on Octic Permutation Polynomials
(in Technical Notes and Short Papers) 450--452
A. C. R. Newbery Multistep Integration Formulas (in
Technical Notes and Short Papers) . . . 452--455
M. Wunderlich On the Non-Existence of Fibonacci
Squares (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 455--457
Hans Riesel A Factor of the Fermat Number ${F}_{19}$
(in Technical Notes and Short Papers) 458--458
Anonymous Corrigenda . . . . . . . . . . . . . . . 487--488
John Gray On Certain Finite Difference Schemes for
Hyperbolic Systems . . . . . . . . . . . 1--18
A. K. Aziz and
B. E. Hubbard Bounds on the Truncation Error by Finite
Differences for the Goursat Problem . . 19--35
M. Stuart Lynn On the Round-Off Error in the Method of
Successive Over-Relaxation . . . . . . . 36--49
J. C. Butcher Implicit Runge--Kutta Processes . . . . 50--64
F. W. J. Olver Error Analysis of Miller's Recurrence
Algorithm . . . . . . . . . . . . . . . 65--74
Daniel Shanks The Second-Order Term in the Asymptotic
Expansion of ${B}(x)$ . . . . . . . . . 75--86
John Brillhart On the Factors of Certain Mersenne
Numbers, II . . . . . . . . . . . . . . 87--92
Donald B. Gillies Three New Mersenne Primes and a
Statistical Theory . . . . . . . . . . . 93--97
W. R. Wilcox Asymptotic Computation of the Repeated
Integrals of the Error Function
Complement . . . . . . . . . . . . . . . 98--105
J. H. Cadwell An Approximation to the Integral of the
Circular Gaussian Distribution over an
Offset Ellipse . . . . . . . . . . . . . 106--112
J. W. Layman A Finite Difference Exponential
Approximation Method (in Technical Notes
and Short Papers) . . . . . . . . . . . 113--118
C. Donald La Budde A New Algorithm for Diagonalizing a Real
Symmetric Matrix (in Technical Notes and
Short Papers) . . . . . . . . . . . . . 118--123
D. B. Hunter The Calculation of Certain Bessel
Functions (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 123--128
Helmut F. Bauer Tables of Zeros of Cross Product Bessel
Functions ${J}_p'(\xi){Y}_p'(k\xi) -
{J}_p'(k\xi){Y}_p'(\xi) = 0$ (in
Technical Notes and Short Papers) . . . 128--135
C. G. Broyden On Convergence Criteria for the Method
of Successive Over-Relaxation (in
Technical Notes and Short Papers) . . . 136--141
Jean L. Lavoie On Inverses of Finite Segments of the
Generalized Hilbert Matrix (in Technical
Notes and Short Papers) . . . . . . . . 141--143
Rosemarie M. Stemmler The Ideal Waring Theorem for Exponents
$401$--$200,000$ (in Technical Notes and
Short Papers) . . . . . . . . . . . . . 144--146
J. L. Selfridge and
Alexander Hurwitz Fermat Numbers and Mersenne Numbers (in
Technical Notes and Short Papers) . . . 146--148
Sidney Kravitz and
Murray Berg Lucas' Test for Mersenne Numbers, $6000 <
p < 7000$ (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 148--149
Hans Riesel Note on the Congruence $a^{p-1} \equiv 1
(\operatorname{mod} p^2)$ (in Technical
Notes and Short Papers) . . . . . . . . 149--150
Milton E. Rose Finite Difference Schemes for
Differential Equations . . . . . . . . . 179--195
Bert K. Larkin Some Stable Explicit Difference
Approximations to the Diffusion Equation 196--202
R. B. Kellogg Difference Equations on a Mesh Arising
from a General Triangulation . . . . . . 203--210
David L. Jagerman The Autocorrelation and Joint
Distribution Functions of the Sequences
$\bigg\{\frac{a}{m}j^2\bigg\},
\bigg\{\frac{a}{m}(j + \tau)^2\bigg\}$ 211--232
J. C. Butcher Integration Processes Based on Radau
Quadrature Formulas . . . . . . . . . . 233--244
T. W. Sag and
G. Szekeres Numerical Evaluation of High-Dimensional
Integrals . . . . . . . . . . . . . . . 245--253
Irwin Roman Controlled Quadrature . . . . . . . . . 254--263
A. C. Ahlin A Bivariate Generalization of Hermite's
Interpolation Formula . . . . . . . . . 264--273
David Elliott The Evaluation and Estimation of the
Coefficients in the Chebyshev Series
Expansion of a Function . . . . . . . . 274--284
Richard Steck A Dynamic Programming Strategy for the
Two Machine Problem . . . . . . . . . . 285--291
A. K. Rigler An Application of Cyclic Reduction to
Ritz Type Difference Equations (in
Technical Notes and Short Papers) . . . 292--296
P. J. Eberlein A Two Parameter Test Matrix (in
Technical Notes and Short Papers) . . . 296--298
B. Mond Multivariate Polynomial Approximation
for Equidistant Data (in Technical Notes
and Short Papers) . . . . . . . . . . . 298--301
Friedrich Gebhardt Generating Normally Distributed Random
Numbers by Inverting the Normal
Distribution Function (in Technical
Notes and Short Papers) . . . . . . . . 302--306
T. E. Hull and
R. L. Johnston Optimum Runge--Kutta Methods (in
Technical Notes and Short Papers) . . . 306--310
Gilbert C. Best Helpful Formulas for Integrating
Polynomials in Three Dimensions (in
Technical Notes and Short Papers) . . . 310--312
Seymour Haber A Note on Some Quadrature Formulas for
the Interval $(-\infty, \infty)$ (in
Technical Notes and Short Papers) . . . 313--314
F. D. Burgoyne Generalized Trigonometric Functions (in
Technical Notes and Short Papers) . . . 314--316
David G. Hummer Expansions of Dawson's Function in a
Series of Chebyshev Polynomials (in
Technical Notes and Short Papers) . . . 317--319
Henry Gerber First One Hundred Zeros of ${J}_0(x)$
Accurate to 19 Significant Figures (in
Technical Notes and Short Papers) . . . 319--322
Daniel Shanks Polylogarithms, Dirichlet Series, and
Certain Constants (in Technical Notes
and Short Papers) . . . . . . . . . . . 322--324
Claude P. Wrathall New Factors of Fermat Numbers (in
Technical Notes and Short Papers) . . . 324--325
Anonymous Corrigendum . . . . . . . . . . . . . . 348--348
James H. Bramble and
Bert E. Hubbard New Monotone Type Approximations for
Elliptic Problems . . . . . . . . . . . 349--367
John McNamee Error-Bounds for the Evaluation of
Integrals by the Euler--Maclaurin
Formula and by Gauss-Type Formulae . . . 368--381
D. G. Moursund Chebyshev Approximations of a Function
and Its Derivatives . . . . . . . . . . 382--389
John R. Rice On the Computation of ${L}_1$
Approximations by Exponentials,
Rationals, and Other Functions . . . . . 390--396
John Brillhart and
D. H. Lehmer and
Emma Lehmer Bounds for Pairs of Consecutive Seventh
and Higher Power Residues . . . . . . . 397--407
V. L. Gardiner and
R. B. Lazarus and
P. R. Stein Solutions of the Diophantine Equation
$x^3 + y^3 = z^3 - d$ . . . . . . . . . 408--413
M. S. Cheema Vector Partitions and Combinatorial
Identities . . . . . . . . . . . . . . . 414--420
A. H. Van Tuyl The Evaluation of Some Definite
Integrals Involving Bessel Functions
Which Occur in Hydrodynamics and
Elasticity . . . . . . . . . . . . . . . 421--432
Chih-Bing Ling and
Chen-Peng Tsai Evaluation at Half Periods of
Weierstrass' Elliptic Function with
Rhombic Primitive Period-Parallelogram 433--440
Boris Podolsky and
Harry H. Denman Conditions on Minimization Criteria for
Smoothing . . . . . . . . . . . . . . . 441--448
M. H. Lietzke and
R. W. Stoughton and
Marjorie P. Lietzke A Comparison of Several Methods for
Inverting Large Symmetric Positive
Definite Matrices . . . . . . . . . . . 449--456
Paul A. White and
Robert R. Brown A Comparison of Methods for Computing
the Eigenvalues and Eigenvectors of a
Real Symmetric Matrix . . . . . . . . . 457--463
Beresford N. Parlett Laguerre's Method Applied to the Matrix
Eigenvalue Problem . . . . . . . . . . . 464--485
George E. Forsythe Tests of Parlett's ALGOL Eigenvalue
Procedure $Eig 3$ (in Technical Notes
and Short Papers) . . . . . . . . . . . 486--487
Richard Bellman and
Robert Kalaba and
Bella Kotkin Differential Approximation Applied to
the Solution of Convolution Equations
(in Technical Notes and Short Papers) 487--491
Henry E. Fettis On the Numerical Solution of Equations
of the Abel Type (in Technical Notes and
Short Papers) . . . . . . . . . . . . . 491--496
W. H. Witty A New Method of Numerical Integration of
Differential Equations (in Technical
Notes and Short Papers) . . . . . . . . 497--500
H. H. Wang and
R. T. Gregory On the Reduction of an Arbitrary Real
Square Matrix to Tridiagonal Form (in
Technical Notes and Short Papers) . . . 501--505
Beresford Parlett A Note on La Budde's Algorithm (in
Technical Notes and Short Papers) . . . 505--506
E. T. Parker and
R. B. Killgrove A Note on Projective Planes of Order
Nine (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 506--508
E. Karst and
U. Karst The First Power of $2$ With $8$
Consecutive Zeros (in Technical Notes
and Short Papers) . . . . . . . . . . . 508--508
Anonymous Corrigenda . . . . . . . . . . . . . . . 536--536
N. G. de Bruijn Some Direct Decompositions of the Set of
Integers . . . . . . . . . . . . . . . . 537--546
Raphael M. Robinson Algebraic Equations with Span Less than
$4$ . . . . . . . . . . . . . . . . . . 547--559
Joel N. Franklin Equidistribution of Matrix-Power
Residues Modulo One . . . . . . . . . . 560--568
Philip J. Davis Triangle Formulas in the Complex Plane 569--577
D. Mustard Numerical Integration over the
$n$-Dimensional Spherical Shell . . . . 578--589
A. H. Stroud Approximate Integration Formulas of
Degree $3$ for Simplexes . . . . . . . . 590--597
T. S. Shao and
T. C. Chen and
R. M. Frank Tables of Zeros and Gaussian Weights of
Certain Associated Laguerre Polynomials
and the Related Generalized Hermite
Polynomials . . . . . . . . . . . . . . 598--616
John R. Rice On the ${L}_\infty$ Walsh Arrays for
${\Gamma}(x)$ and $\mathrm{Erfc}(x)$ . . 617--626
Wyman Fair Padé Approximation to the Solution of the
Ricatti Equation . . . . . . . . . . . . 627--634
A. B. Otis, Jr. and
M. P. Barnett Surface Harmonic Expansions of Products
of Cartesian Coordinates . . . . . . . . 635--643
P. Erd\Hos On a Problem in Elementary Number Theory
and a Combinatorial Problem (in
Technical Notes and Short Papers) . . . 644--646
Daniel Shanks On Maximal Gaps between Successive
Primes (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 646--651
Lester J. Senechalle Iteration of Triangular Matrices (in
Technical Notes and Short Papers) . . . 651--653
Jean L. Lavoie On the Evaluation of Certain
Determinants (in Technical Notes and
Short Papers) . . . . . . . . . . . . . 653--659
R. W. Klopfenstein Conditional Least Squares Polynomial
Approximation (in Technical Notes and
Short Papers) . . . . . . . . . . . . . 659--662
D. van Z. Wadsworth Improved Asymptotic Expansion for the
Error Function with Imaginary Argument
(in Technical Notes and Short Papers) 662--664
J. T. Day A One-Step Method for the Numerical
Solution of Second Order Linear Ordinary
Differential Equations (in Technical
Notes and Short Papers) . . . . . . . . 664--668
Donald D. Fisher Minimum Ellipsoids (in Technical Notes
and Short Papers) . . . . . . . . . . . 669--673
R. P. Boas, Jr. and
Virginia C. Klema A Constant in the Theory of
Trigonometric Series (in Technical Notes
and Short Papers) . . . . . . . . . . . 674--674
Anonymous Corrigendum . . . . . . . . . . . . . . 688--688
Olof B. Widlund On the Stability of Parabolic Difference
Schemes . . . . . . . . . . . . . . . . 1--13
M. Z. Nashed On General Iterative Methods for the
Solutions of a Class of Nonlinear
Operator Equations . . . . . . . . . . . 14--24
David Elliott and
George Szekeres Some Estimates of the Coefficients in
the Chebyshev Series Expansion of a
Function . . . . . . . . . . . . . . . . 25--32
Francis J. Smith An Algorithm for Summing Orthogonal
Polynomial Series and their Derivatives
with Applications to Curve-Fitting and
Interpolation . . . . . . . . . . . . . 33--36
W. V. Petryshyn On the Extrapolated Jacobi or
Simultaneous Displacements Method in the
Solution of Matrix and Operator
Equations . . . . . . . . . . . . . . . 37--55
A. J. Hoffman On the Nonsingularity of Real Matrices 56--61
N. A. Derzko and
A. M. Pfeffer Bounds for the Spectral Radius of a
Matrix . . . . . . . . . . . . . . . . . 62--67
M. H. McAndrew An Algorithm for Solving a Polynomic
Congruence, and its Application to
Error-Correcting Cods . . . . . . . . . 68--72
Harry S. Hayashi Computer Investigation of Difference
Sets . . . . . . . . . . . . . . . . . . 73--78
Don Secrest Best Approximate Integration Formulas
and Best Error Bounds . . . . . . . . . 79--83
Hans J. Stetter Stabilizing Predictors for Weakly
Unstable Correctors . . . . . . . . . . 84--89
Robert R. Brown and
James D. Riley and
Morris M. Bennett Stability Properties of Adams-Moulton
Type Methods . . . . . . . . . . . . . . 90--96
Henry E. Fettis Calculation of Elliptic Integrals of the
Third Kind by Means of Gauss'
Transformation . . . . . . . . . . . . . 97--104
W. J. Cody Chebyshev Approximations for the
Complete Elliptic Integrals ${K}$ and
${E}$ . . . . . . . . . . . . . . . . . 105--112
R. G. Medhurst and
J. H. Roberts Evaluation of the Integral ${I}_n(b) =
\frac{2}{\pi} \int^\infty_0
\bigg(\frac{\sin x}{x}\bigg)^n \cos (bx)
dx$ . . . . . . . . . . . . . . . . . . 113--117
A. H. Heatley An Extension of the Table of the Toronto
Function (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 118--123
Chih-Bing Ling Tables of Values of $\sigma_{2s}$
Relating to Weierstrass' Elliptic
Function (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 123--127
Otto Neall Strand A Method for the Computation of the
Error Function of a Complex Variable (in
Technical Notes and Short Papers) . . . 127--129
P. Razelos A New Integral Representation of the
Bessel Coefficients (in Technical Notes
and Short Papers) . . . . . . . . . . . 130--133
Y. T. Lo and
S. W. Lee and
B. Sun On Davis' Method of Estimating
Quadrature Errors (in Technical Notes
and Short Papers) . . . . . . . . . . . 133--138
Donald W. L. Sprung and
D. J. Hughes Gauss Weights and Ordinates for
$\int^1_0 f(x)x^2 dx$ (in Technical
Notes and Short Papers) . . . . . . . . 139--142
Alan G. Konheim Mantissa Distributions (in Technical
Notes and Short Papers) . . . . . . . . 143--144
A Gloden New Primes of the Form $n^4 + 1$ (in
Technical Notes and Short Papers) . . . 144--145
K. R. Isemonger Some Additional Factorizations of $2^n
\pm 1$ (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 145--146
Anonymous Corrigenda . . . . . . . . . . . . . . . 175--175
J. F. Traub Generalized Sequences with Applications
to the Discrete Calculus . . . . . . . . 177--200
Robert C. Tausworthe Random Numbers Generated by Linear
Recurrence Modulo Two . . . . . . . . . 201--209
Raphael M. Robinson Some Conjectures About Cyclotomic
Integers . . . . . . . . . . . . . . . . 210--217
Burton Wendroff Bounds for Eigenvalues of Some
Differential Operators by the
Rayleigh--Ritz Method . . . . . . . . . 218--224
Lloyd D. Fosdick Approximation of a Class of Wiener
Integrals . . . . . . . . . . . . . . . 225--233
David Elliott Truncation Errors in Two Chebyshev
Series Approximations . . . . . . . . . 234--248
W. J. Cody Chebyshev Polynomial Expansions of
Complete Elliptic Integrals . . . . . . 249--259
J. N. Lyness Symmetric Integration Rules for
Hypercubes I. Error Coefficients . . . . 260--276
E. L. Whitney Estimates of Weights in Gauss-Type
Quadrature . . . . . . . . . . . . . . . 277--286
C. R. Cassity Abscissas, Coefficients, and Error Term
for the Generalized Gauss--Laguerre
Quadrature Formula Using the Zero
Ordinate . . . . . . . . . . . . . . . . 287--296
James W. Cooley and
John W. Tukey An Algorithm for the Machine Calculation
of Complex Fourier Series . . . . . . . 297--301
A. K. Rigler Estimation of the Successive
Over-Relaxation Factor (in Technical
Notes and Short Papers) . . . . . . . . 302--307
H. S. Price A Practical Application of Block
Diagonally Dominant Matrices (in
Technical Notes and Short Papers) . . . 307--313
John Gary Hyman's Method Applied to the General
Eigenvalue Problem (in Technical Notes
and Short Papers) . . . . . . . . . . . 314--316
A. D. Keedwell A Search for Projective Planes of a
Special Type with the Aid of a Digital
Computer (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 317--322
Nancy Lee and
A. H. Stroud Approximate Integration Formulas for
Ellipses (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 322--327
Donald van Zelm Wadsworth Improved Asymptotic Expansion for the
Exponential Integral with Positive
Argument (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 327--328
Irving H. Siegel Deferment of Computation in the Method
of Least Squares (in Technical Notes and
Short Papers) . . . . . . . . . . . . . 329--331
Daniel Shanks Review of: Marshall Hall, Jr. and James
K. Senior, ``The Groups of Order $2^n (n
\le 6)$'' . . . . . . . . . . . . . . . 335--337
John Gary Computing Eigenvalues of Ordinary
Differential Equations by Finite
Differences . . . . . . . . . . . . . . 365--379
L. M. Delves Variation Principles for an Arbitrary
Operator. III . . . . . . . . . . . . . 380--386
W. E. Simon Numerical Technique for Solution and
Error Estimate for the Initial Value
Problem . . . . . . . . . . . . . . . . 387--393
J. N. Lyness Symmetric Integration Rules for
Hypercubes II. Rule Projection and Rule
Extension . . . . . . . . . . . . . . . 394--407
J. C. Butcher On the Attainable Order of Runge--Kutta
Methods . . . . . . . . . . . . . . . . 408--417
D. L. Jagerman Some Theorems Concerning Pseudo-Random
Numbers . . . . . . . . . . . . . . . . 418--426
M. L. Stein and
P. R. Stein Experimental Results on Additive
$2$-Bases . . . . . . . . . . . . . . . 427--434
N. Metropolis and
R. L. Ashenhurst Radix Conversion in an Unnormalized
Arithmetic System . . . . . . . . . . . 435--441
L. D. Baumert and
Marshall Hall, Jr. Hadamard Matrices of the Williamson Type 442--447
R. B. Kellogg and
J. Spanier On Optimal Alternating Direction
Parameters for Singular Matrices (in
Technical Notes and Short Papers) . . . 448--452
Adi Ben-Israel An Iterative Method for Computing the
Generalized Inverse of an Arbitrary
Matrix (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 452--455
C. H. Yang A Note on the Maximum Value of
Determinants Over the Complex Field (in
Technical Notes and Short Papers) . . . 455--456
John D. Lambert and
Brian Shaw On the Numerical Solution of $y' = f(x,
y)$ by a Class of Formulae Based on
Rational Approximation (in Technical
Notes and Short Papers) . . . . . . . . 456--462
Theodore R. Goodman The Numerical Solution of Eigenvalue
Problems (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 462--466
V. O. S. Olunloyo A Special Technique for the
Determination of Eigenvalues (in
Technical Notes and Short Papers) . . . 466--471
J. N. Lyness Integration Rules of Hypercubic Symmetry
Over a Certain Spherically Symmetric
Space (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 471--476
Donald G. Anderson Gaussian Quadrature Formulae for
$\int^1_0 -ln(x)f(x) dx$ (in Technical
Notes and Short Papers) . . . . . . . . 477--481
Lawrence F. Shampine Quadrature Formulas Using Derivatives
(in Technical Notes and Short Papers) 481--482
Jacqueline Wells and
Joseph Muskat On the Number of Solutions of Certain
Trinomial Congruences (in Technical
Notes and Short Papers) . . . . . . . . 483--487
Chih-Bing Ling and
Hsien-Chueh Wu Tables of Values of Three Infinite
Integrals (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 487--494
Charles H. Franke Numerical Evaluation of the Elliptic
Integral of the Third Kind (in Technical
Notes and Short Papers) . . . . . . . . 494--496
Wendy James and
P. Jarratt The Generation of Square Roots on a
Computer with Rapid Multiplication
Compared with Division (in Technical
Notes and Short Papers) . . . . . . . . 497--500
Robert F. Church On a Constant in the Theory of
Trigonometric Series (in Technical Notes
and Short Papers) . . . . . . . . . . . 501--501
Yudell L. Luke and
Wyman Fair and
Gerald ine Coombs and
Rosemary Moran On a Constant in the Theory of
Trigonometric Series (in Technical Notes
and Short Papers) . . . . . . . . . . . 501--502
Anonymous Errata . . . . . . . . . . . . . . . . . 527--528
Anonymous Corrigendum . . . . . . . . . . . . . . 529--529
R. J. Aumann and
B. Peleg and
P. Rabinowitz A Method for Computing the Kernel of
$n$-Person Games . . . . . . . . . . . . 531--551
Joel N. Franklin Difference Methods for Stochastic
Ordinary Differential Equations . . . . 552--561
H. M. Sternberg and
J. B. Diaz Computation of the Riemann Function for
the Operator $\partial^n/ \partial
x_1\partial x_2 \cdots \partial x_n +
a(x_1, x_2, \cdots, x_n)$ . . . . . . . 562--569
Carl E. Pearson Impulsive End Condition for Diffusion
Equation . . . . . . . . . . . . . . . . 570--576
C. G. Broyden A Class of Methods for Solving Nonlinear
Simultaneous Equations . . . . . . . . . 577--593
Harvey Cohn A Numerical Survey of the Floors of
Various Hilbert Fundamental Domains . . 594--605
Jerry L. Fields Rational Approximations to Generalized
Hypergeometric Functions . . . . . . . . 606--624
J. N. Lyness Symmetric Integration Rules for
Hypercubes III. Construction of
Integration Rules Using Null Rules . . . 625--637
J. N. Lyness Limits on the Number of Function
Evaluations Required by Certain
High-Dimensional Integration Rules of
Hypercubic Symmetry . . . . . . . . . . 638--643
B. H. Mayoh A Graph Technique for Inverting Certain
Matrices (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 644--646
Stephan Ormonde and
Jerald S. Dick A Method of Calculation of Integrals of
Products of Radial Atomic Wave Functions
(in Technical Notes and Short Papers) 647--650
Jerry Allan Roberts Computation of Moments of
${K}_\nu(t)/{I}_\nu(t)$ (in Technical
Notes and Short Papers) . . . . . . . . 651--654
Lawrence R. Mack Bessel-Function Identities Needed for
the Theory of Axisymmetric Gravity Waves
(in Technical Notes and Short Papers) 654--657
Chih-Bing Ling Evaluation at Half Periods of
Weierstrass' Elliptic Functions with
Double Periods $1$ and $e^{i\alpha}$ (in
Technical Notes and Short Papers) . . . 658--661
G. T. Thompson The Asymptotic Expansion of the
Integrals Psi and Chi in Terms of
Tchebycheff Polynomials (in Technical
Notes and Short Papers) . . . . . . . . 661--663
Arun Verma A Class of Expansions of ${G}$-Functions
and the Laplace Transform (in Technical
Notes and Short Papers) . . . . . . . . 664--666
L. Carlitz The Irreducibility of the Bernoulli
Polynomial ${B}_{14}(x)$ (in Technical
Notes and Short Papers) . . . . . . . . 667--670
H. C. Williams and
R. A. German and
C. R. Zarnke Solution of the Cattle Problem of
Archimedes (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 671--674
Selmer M. Johnson An Elementary Remark on Maximal Gaps
Between Successive Primes (in Technical
Notes and Short Papers) . . . . . . . . 675--676
Bogumil Leszczynski On the Sum of the Series
$\sum^\infty_{\nu = 0} (t^\nu/\lbrack
u\nu + m \rbrack!)$ (in Technical Notes
and Short Papers) . . . . . . . . . . . 677--679
Daniel Shanks Review of Paul T. Bateman and Roger A.
Horn, ``Primes Represented by
irreducible polynomials in one
variable'', in \em Theory of Numbers,
pp. 119--132, in particular Tables II--V 684--686
Anonymous Errata . . . . . . . . . . . . . . . . . 705--706
Anonymous Corrigendum . . . . . . . . . . . . . . 706--706
J. C. Butcher On the Convergence of Numerical
Solutions to Ordinary Differential
Equations . . . . . . . . . . . . . . . 1--10
J. D. Lambert and
B. Shaw A Method for the Numerical Solution of
$y' = f(x, y)$ Based on a Self-Adjusting
Non-Polynomial Interpolant . . . . . . . 11--20
E. Baylis Shanks Solutions of Differential Equations by
Evaluations of Functions . . . . . . . . 21--38
Charles E. Treanor A Method for the Numerical Integration
of Coupled First-Order Differential
Equations with Greatly Different Time
Constants . .