generalized%20hypergeometric%20functions

SearchAdvancedHelp

(0.007 seconds)

11—18 of 18 matching pages

11: Bibliography P

… ►

A Kummer-type transformation for a ${}_2{}^{}F_2^{}$ hypergeometric function. J. Comput. Appl. Math. 173 (2), pp. 379–382.

ⓘ

External Links:

ISSN 0377-0427, Document, MathReview (P. Anandani), ZentralBlatt

Referenced by:

§16.6.

Encodings:

BibTeX

… ►

Exponentially small expansions of the confluent hypergeometric functions. Appl. Math. Sci. (Ruse) 7 (133-136), pp. 6601–6609.

ⓘ

External Links:

ISSN 1312-885X, Document, MathReview Entry

Referenced by:

§13.7(iii), §13.7(iii).

Encodings:

BibTeX

… ►

A numerical evaluator for the generalized hypergeometric series. Comput. Phys. Comm. 77 (2), pp. 249–254.

ⓘ

Notes:

Extended-precision Fortran, maximum accuracy 12D.

External Links:

Document, Code, ZentralBlatt

Referenced by:

1st item.

Encodings:

BibTeX

… ►

Numerical calculation of the generalized Fermi-Dirac integrals. Comput. Phys. Comm. 55 (2), pp. 127–136.

ⓘ

External Links:

Document

Referenced by:

§25.18(i).

Encodings:

BibTeX

… ►

Automatic computation of Bessel function integrals. Comput. Phys. Comm. 25 (3), pp. 289–295.

ⓘ

Notes:

Double-precision Fortran, maximum accuracy 20S.

External Links:

ISSN 0010-4655, Document, Code

Referenced by:

6th item.

Encodings:

BibTeX

…

12: Bibliography M

… ►

Hypergeometric Functions.

ⓘ

Notes:

Unpublished Lecture Notes, University of London. An online version exists.

External Links:

FullText

Referenced by:

§35.7(ii), §35.8(iii).

Encodings:

BibTeX

… ►

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

ⓘ

External Links:

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

Referenced by:

§10.74(iii).

Encodings:

BibTeX

… ►

Euler-type transformations for the generalized hypergeometric function ${}_{r+2}{}^{}F_{r+1}^{}(x)$ . Z. Angew. Math. Phys. 62 (1), pp. 31–45.

ⓘ

External Links:

ISSN 0044-2275, Document, FullText, MathReview (Mridula Garg), ZentralBlatt

Referenced by:

§16.6, §16.6.

Encodings:

BibTeX

►

A class of generalized hypergeometric summations. J. Comput. Appl. Math. 87 (1), pp. 79–85.

ⓘ

External Links:

ISSN 0377-0427, Document, MathReview, ZentralBlatt

Referenced by:

§16.10.

Encodings:

BibTeX

►

On a Kummer-type transformation for the generalized hypergeometric function ${}_2{}^{}F_2^{}$ . J. Comput. Appl. Math. 157 (2), pp. 507–509.

ⓘ

External Links:

ISSN 0377-0427, Document, MathReview Entry, ZentralBlatt

Referenced by:

§16.6.

Encodings:

BibTeX

…

13: Errata

… ►

A note about the multivalued nature of the Kummer confluent hypergeometric function of the second kind $U$ on the right-hand side of (7.18.10) was inserted.

… ►

Confluent hypergeometric functions were incorrectly linked to the definitions of the Kummer confluent hypergeometric and parabolic cylinder functions. However, to the eye, the functions appeared correct. The links were corrected.

… ►

The Wronskian was generalized to include both associated Legendre and Ferrers functions.

… ►

Several new equations have been added. See (8.17.24), (20.7.34), §20.11(v), (26.12.27), (36.2.28), and (36.2.29).

… ►

Bibliographic citations were added in §§1.13(v), 10.14, 10.21(ii), 18.15(v), 18.32, 30.16(iii), 32.13(ii), and as general references in Chapters 19, 20, 22, and 23.

…

14: 18.5 Explicit Representations

… ►

§18.5(i) Trigonometric Functions

… ►

§18.5(iii) Finite Power Series, the Hypergeometric Function, and Generalized Hypergeometric Functions

►For the definitions of ${}_2{}^{}F_1^{}$, ${}_1{}^{}F_1^{}$, and ${}_2{}^{}F_0^{}$ see §16.2. … ►

Laguerre

… ►

Hermite

…

15: Bibliography S

… ►

Transformations of the Jacobian amplitude function and its calculation via the arithmetic-geometric mean. SIAM J. Math. Anal. 20 (6), pp. 1514–1528.

ⓘ

External Links:

ISSN 0036-1410, Document, MathReview (J. M. H. Peters), ZentralBlatt

Referenced by:

§22.19(i), §22.20(vi).

Encodings:

BibTeX

… ►

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

ⓘ

External Links:

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

Referenced by:

§28.8(iv).

Encodings:

BibTeX

… ►

Generalized Hypergeometric Functions. Cambridge University Press, Cambridge.

ⓘ

External Links:

ISBN 9780521090612, MathReview (S. C. van Veen), ZentralBlatt

Referenced by:

Ch.15, §16.2(iii), §16.4(ii), §16.4(iii), §16.4(v), Ch.16, §17.1, §17.4(i), Ch.17.

Encodings:

BibTeX

… ►

On the logarithmic solutions of the generalized hypergeometric equation when $p=q+1$ . Bull. Amer. Math. Soc. 45 (8), pp. 629–636.

ⓘ

External Links:

Document, MathReview (H. Bateman), ZentralBlatt

Referenced by:

§16.8(ii).

Encodings:

BibTeX

… ►

Computation of angular momentum coefficients using sets of generalized hypergeometric functions. Comput. Phys. Comm. 22 (2-3), pp. 297–302.

ⓘ

External Links:

Document

Referenced by:

§34.13.

Encodings:

BibTeX

…

16: Bibliography G

… ►

On the generalization of a method for computing Bessel function integrals. J. Comput. Appl. Math. 6 (2), pp. 167–168.

ⓘ

External Links:

ISSN 0771-050X, Document, MathReview, ZentralBlatt

Referenced by:

§10.74(vii).

Encodings:

BibTeX

… ►

Gauss quadrature approximations to hypergeometric and confluent hypergeometric functions. J. Comput. Appl. Math. 139 (1), pp. 173–187.

ⓘ

External Links:

ISSN 0377-0427, Document, MathReview (Hasan Taşeli), ZentralBlatt

Referenced by:

§13.29(iii), §15.19(iii).

Encodings:

BibTeX

… ►

Generalized Functions. Vol. 1: Properties and Operations. Academic Press, New York.

ⓘ

Notes:

Translated from the Russian by Eugene Saletan. A paperbound reprinting by the same publisher appeared in 1977

External Links:

MathReview, ZentralBlatt

Referenced by:

§2.6(i).

Encodings:

BibTeX

… ►

Algorithm 939: computation of the Marcum Q-function. ACM Trans. Math. Softw. 40 (3), pp. 20:1–20:21.

ⓘ

Notes:

Includes Fortran program claiming 12S accuracy

External Links:

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

Referenced by:

3rd item, §10.77(ix).

Encodings:

BibTeX

… ►

Generalized Fermi-Dirac functions and derivatives: Properties and evaluation. Comput. Phys. Comm. 136 (3), pp. 294–309.

ⓘ

Notes:

Double-precision Fortran, maximum accuracy 20D

External Links:

Document, Code, ZentralBlatt

Referenced by:

7th item.

Encodings:

BibTeX

…

17: 20.11 Generalizations and Analogs

§20.11 Generalizations and Analogs

… ► … ►Similar identities can be constructed for ${}_2{}^{}F_1^{}(\frac{1}{3},\frac{2}{3};1;k^2)$, ${}_2{}^{}F_1^{}(\frac{1}{4},\frac{3}{4};1;k^2)$, and ${}_2{}^{}F_1^{}(\frac{1}{6},\frac{5}{6};1;k^2)$. …For applications to rapidly convergent expansions for $\pi$ see Chudnovsky and Chudnovsky (1988), and for applications in the construction of elliptic-hypergeometric series see Rosengren (2004). ►

§20.11(iv) Theta Functions with Characteristics

…

18: Bibliography L

… ►

Algorithm 917: complex double-precision evaluation of the Wright $\omega$ function. ACM Trans. Math. Software 38 (3), pp. Art. 20, 17.

ⓘ

External Links:

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

Referenced by:

§4.13, 2nd item, §4.48(iv).

Encodings:

BibTeX

… ►

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

ⓘ

External Links:

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

Referenced by:

§16.4(iii).

Encodings:

BibTeX

… ►

Jacobi polynomial expansions of a generalized hypergeometric function over a semi-infinite ray. Math. Comp. 17 (84), pp. 395–404.

ⓘ

External Links:

FullText, MathReview (I. A. Stegun), ZentralBlatt

Referenced by:

2nd item.

Encodings:

BibTeX

►

Expansion of the confluent hypergeometric function in series of Bessel functions. Math. Tables Aids Comput. 13 (68), pp. 261–271.

ⓘ

External Links:

FullText, MathReview (A. Erdélyi), ZentralBlatt

Referenced by:

§13.24(ii).

Encodings:

BibTeX

… ►

Algorithms for rational approximations for a confluent hypergeometric function. Utilitas Math. 11, pp. 123–151.

ⓘ

External Links:

MathReview (F. Gotze), ZentralBlatt

Referenced by:

§13.31(iii).

Encodings:

BibTeX

…