Coulomb%20spheroidal%20functions

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1: Software Index

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	Open Source													With Book						Commercial
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20 Theta Functions
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►‘✓’ indicates that a software package implements the functions in a section; ‘a’ indicates available functionality through optional or add-on packages; an empty space indicates no known support. … ►In the list below we identify four main sources of software for computing special functions. … ►

Such software ranges from a collection of reusable software parts (e.g., a library) to fully functional interactive computing environments with an associated computing language. Such software is usually professionally developed, tested, and maintained to high standards. It is available for purchase, often with accompanying updates and consulting support.

… ►The following are web-based software repositories with significant holdings in the area of special functions. …

2: Bibliography B

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An algorithm for regular and irregular Coulomb and Bessel functions of real order to machine accuracy. Comput. Phys. Comm. 21 (3), pp. 297–314.

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External Links:

Document

Referenced by:

§3.10(iii), §33.22(iv).

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Coulomb functions (negative energies). Comput. Phys. Comm. 20 (3), pp. 447–458.

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Notes:

Double-precision Fortran code.

External Links:

Document, Code

Referenced by:

1st item, 4th item.

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Prolate angular spheroidal wave functions. Comput. Phys. Comm. 30 (2), pp. 187–192.

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Document, Code

Referenced by:

1st item.

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Prolate radial spheroidal wave functions. Comput. Phys. Comm. 30 (2), pp. 177–185.

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Document, Code

Referenced by:

1st item.

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On spheroidal wave functions of order zero. J. Math. Phys. Mass. Inst. Tech. 26, pp. 79–92.

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External Links:

ISSN 0097-1421, MathReview (M. J. O. Strutt), ZentralBlatt

Referenced by:

§30.16(i).

Encodings:

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3: Bibliography

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Exact linearization of a Painlevé transcendent. Phys. Rev. Lett. 38 (20), pp. 1103–1106.

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External Links:

Document, MathReview (Mark Adler)

Referenced by:

§32.11(ii), §32.13(i), §32.13(ii), §32.13(iii), §32.5.

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Evaluation of Coulomb wave functions along the transition line. Physical Rev. (2) 96, pp. 77–79.

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External Links:

Document, MathReview (A. Erdélyi), ZentralBlatt

Referenced by:

§33.12(i).

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Asymptotic expansions of spheroidal wave functions. J. Math. Phys. Mass. Inst. Tech. 28, pp. 195–199.

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External Links:

MathReview (J. G. van der Corput), ZentralBlatt

Referenced by:

§30.9(iii).

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Regular and irregular Coulomb wave functions expressed in terms of Bessel-Clifford functions. J. Math. Physics 33, pp. 111–116.

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External Links:

MathReview (E. Weber), ZentralBlatt

Referenced by:

§33.9(ii).

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Repeated integrals and derivatives of $K$ Bessel functions. SIAM J. Math. Anal. 20 (1), pp. 169–175.

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External Links:

ISSN 0036-1410, Document, MathReview (A. Haimovici), ZentralBlatt

Referenced by:

§10.43(iii).

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4: Bibliography M

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Calculation of the modified Bessel functions of the second kind with complex argument. Math. Comp. 20 (95), pp. 407–412.

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External Links:

ISSN 0025-5718, FullText, MathReview (H. E. Fettis), ZentralBlatt

Referenced by:

§10.74(iii).

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Precise Coulomb wave functions for a wide range of complex $\mathrm{\ell }$, $\eta$ and $z$ . Computer Physics Communications 176 (3), pp. 232–249.

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Notes:

C++ code. Maximum accuracy 10D

External Links:

Document, Code, ZentralBlatt

Referenced by:

1st item.

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Asymptotic approximations for prolate spheroidal wave functions. Studies in Appl. Math. 54 (4), pp. 315–349.

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External Links:

MathReview (M. L. Mehta), ZentralBlatt

Referenced by:

§30.9(i).

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Asymptotic expansions of oblate spheroidal wave functions and their characteristic numbers. J. Reine Angew. Math. 211, pp. 33–47.

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External Links:

MathReview (J. Meixner), ZentralBlatt

Referenced by:

§30.9(ii), §30.9(ii).

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Asymptotic expansions of prolate spheroidal wave functions and their characteristic numbers. J. Reine Angew. Math. 212, pp. 26–48.

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External Links:

MathReview (J. Meixner), ZentralBlatt

Referenced by:

§30.9(i), §30.9(i).

Encodings:

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5: Bibliography C

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Coulomb phase shift. American Journal of Physics 47 (8), pp. 683–684.

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External Links:

Document

Referenced by:

§5.20.

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Validated computation of certain hypergeometric functions. ACM Trans. Math. Software 38 (2), pp. Art. 11, 20.

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External Links:

ISSN 0098-3500, Document, FullText, MathReview Entry, ZentralBlatt

Referenced by:

§13.29(v), §15.19(v).

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Product formulas and convolutions for angular and radial spheroidal wave functions. Trans. Amer. Math. Soc. 338 (2), pp. 695–710.

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External Links:

ISSN 0002-9947, FullText, MathReview (Jean-Claude Lucquiaud), ZentralBlatt

Referenced by:

§30.10, §30.11(vi).

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Coulomb effects in the Klein-Gordon equation for pions. Phys. Rev. C 20 (2), pp. 696–704.

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External Links:

Document

Referenced by:

5th item.

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Coulomb Wave Functions. Roy. Soc. Math. Tables, Vol. 11, Cambridge University Press, Cambridge.

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External Links:

ISBN 0-521-06156-3, MathReview (John Todd), ZentralBlatt

Referenced by:

item Curtis (1964a):, §33.14(i), §33.20(iv), §33.21(ii), §33.23(vi), 2nd item, §33.9(ii), Notations P, Notations Q.

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6: Bibliography K

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Algorithm 737: INTLIB: A portable Fortran 77 interval standard-function library. ACM Trans. Math. Software 20 (4), pp. 447–459.

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External Links:

ISSN 0098-3500, Document, GAMS (module 737; package TOMS), ZentralBlatt

Referenced by:

1st item.

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Methods of computing the Riemann zeta-function and some generalizations of it. USSR Comput. Math. and Math. Phys. 20 (6), pp. 212–230.

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External Links:

Document, MathReview (Matti Jutila), ZentralBlatt

Referenced by:

§25.18(i).

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A Fortran computer program for calculating the prolate spheroidal radial functions of the first and second kind and their first derivatives. NRL Report No. 7012 Naval Res. Lab.  Washingtion, D.C..

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Referenced by:

§30.18(iii).

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A general addition theorem for spheroidal wave functions. SIAM J. Math. Anal. 4 (1), pp. 149–160.

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External Links:

Document, MathReview (J. Meixner), ZentralBlatt

Referenced by:

§30.10.

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Sferoidalnye i kulonovskie sferoidalnye funktsii. Izdat. “Nauka”, Moscow (Russian).

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Notes:

Translated title: Spheroidal and Coulomb Spheroidal Functions

External Links:

MathReview

Referenced by:

§30.12, Ch.30, §31.13.

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