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11: Bibliography

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Tables of $\ln \mathrm{\Gamma }(z)$ for Complex Argument. Pergamon Press, New York.

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External Links:

ZentralBlatt

Referenced by:

§5.22(iii).

Encodings:

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Numerical evaluation of the Kummer function with complex argument by the trapezoidal rule. Rend. Sem. Mat. Univ. Politec. Torino 49 (3), pp. 315–327.

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External Links:

ISSN 0373-1243, MathReview, ZentralBlatt

Referenced by:

§13.29(iii).

Encodings:

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A subroutine package for Bessel functions of a complex argument and nonnegative order. Technical Report Technical Report SAND85-1018, Sandia National Laboratories, Albuquerque, NM.

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External Links:

FullText

Referenced by:

1st item, B. Döring (1966).

Encodings:

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Algorithm 644: A portable package for Bessel functions of a complex argument and nonnegative order. ACM Trans. Math. Software 12 (3), pp. 265–273.

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Notes:

Single and double precision, maximum accuracy 18S.

External Links:

ISSN 0098-3500, Document, Remark #1. Remark #2. GAMS (module 644; package TOMS), MathReview Entry, ZentralBlatt

Referenced by:

1st item, 1st item, 2nd item, 1st item.

Encodings:

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Algorithm 683: A portable FORTRAN subroutine for exponential integrals of a complex argument. ACM Trans. Math. Software 16 (2), pp. 178–182.

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Notes:

Double- and single-precision Fortran, maximum accuracy 18S or 14S.

External Links:

ISSN 0098-3500, Document, GAMS (module 683; package TOMS), MathReview, ZentralBlatt

Referenced by:

1st item, 1st item.

Encodings:

BibTeX

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12: 35.10 Methods of Computation

§35.10 Methods of Computation

… ►See Yan (1992) for the ${}_1{}^{}F_1^{}$ and ${}_2{}^{}F_1^{}$ functions of matrix argument in the case $m=2$, and Bingham et al. (1992) for Monte Carlo simulation on $𝐎(m)$ applied to a generalization of the integral (35.5.8). …

13: 35 Functions of Matrix Argument

Chapter 35 Functions of Matrix Argument

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14: Bibliography L

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Recurrence relations for hypergeometric functions of unit argument. Math. Comp. 45 (172), pp. 521–535.

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External Links:

ISSN 0025-5718, FullText, MathReview (S. Conde), ZentralBlatt

Referenced by:

§16.4(iii).

Encodings:

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Corrigenda: “Recurrence relations for hypergeometric functions of unit argument” [Math. Comp. 45 (1985), no. 172, 521–535; MR 86m:33004]. Math. Comp. 48 (178), pp. 853.

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External Links:

ISSN 0025-5718, FullText, MathReview, ZentralBlatt

Referenced by:

§16.4(iii).

Encodings:

BibTeX

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Computations of spheroidal harmonics with complex arguments: A review with an algorithm. Phys. Rev. E 58 (5), pp. 6792–6806.

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Notes:

Mathematica package for eigenvalues and solutions of the spheroidal wave equations

External Links:

Code(SpheroidF), Document

Referenced by:

2nd item, 3rd item.

Encodings:

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On Bessel functions of equal order and argument. Rend. Sem. Mat. Univ. Politec. Torino 50 (2), pp. 209–216 (1993).

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External Links:

ISSN 0373-1243, MathReview (N. Hayek Calil), ZentralBlatt

Referenced by:

§10.14.

Encodings:

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The Principle of Relativity: A Collection of Original Memoirs on the Special and General Theory of Relativity. Methuen and Co., Ltd., London.

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Notes:

Translated from Das Relativitätsprinzip by W. Perrett and G. B. Jeffery. Reprinted by Dover Publications Inc., New York, 1952.

External Links:

MathReview, ZentralBlatt

Referenced by:

§1.6(ii).

Encodings:

BibTeX

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15: 20.16 Software

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§20.16(ii) Real Argument and Parameter

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§20.16(iii) Complex Argument and/or Parameter

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16: 22.22 Software

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§22.22(ii) Real Argument

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§22.22(iii) Complex Argument

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17: 1.10 Functions of a Complex Variable

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Schwarz Reflection Principle

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Phase (or Argument) Principle

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§1.10(v) Maximum-Modulus Principle

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Analytic Functions

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Harmonic Functions

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18: Software Index

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	Open Source													With Book						Commercial
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16.27(ii) Real Arguments	✓		✓		✓	✓						a	✓								✓	✓	✓
16.27(iii) Complex Arguments	✓											a	✓								✓	✓	✓
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22.22(ii) Real Argument	✓		✓		✓	✓		✓				✓	✓	✓		✓	✓		✓	✓	✓	✓	✓	✓
22.22(iii) Complex Argument	✓					✓						✓	✓	✓						✓	✓	✓	a	✓
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23.24(ii) Real Argument																					✓	✓	a
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19: 18.39 Applications in the Physical Sciences

… ►which is the quantum superposition principle. … … ►argument a) The Harmonic Oscillator … ►argument … ►where $n$ is now the Bohr Principle Quantum Number. …

20: Bibliography S

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Parabolic cylinder functions of integer and half-integer orders for nonnegative arguments. Comput. Phys. Comm. 115 (1), pp. 69–86.

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Notes:

Double-precision Fortran, minimum accuracy 14S, maximum accuracy 18D.

External Links:

ISSN 0010-4655, Document, Code, MathReview, ZentralBlatt

Referenced by:

3rd item.

Encodings:

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Uniform asymptotic forms of modified Mathieu functions. Quart. J. Mech. Appl. Math. 20 (3), pp. 365–380.

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External Links:

Document, MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§28.8(iv).

Encodings:

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Principles of Atomic Spectra. John Wiley & Sons Ltd., New York.

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External Links:

ISBN 0-471-78835-X

Referenced by:

§34.12.

Encodings:

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Inequalities involving cylindrical functions of nearly equal argument and order. Proc. Amer. Math. Soc. 5 (3), pp. 337–344.

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External Links:

ISSN 0002-9939, FullText, MathReview (N. D. Kazarinoff), ZentralBlatt

Referenced by:

§10.14.

Encodings:

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An inequality involving Bessel functions of argument nearly equal to their order. Proc. Amer. Math. Soc. 4 (6), pp. 858–859.

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External Links:

ISSN 0002-9939, FullText, MathReview (N. D. Kazarinoff), ZentralBlatt

Referenced by:

§10.14.

Encodings:

BibTeX

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