extensions of Kummer relations

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1: 16.4 Argument Unity

… ►The other three-term relations are extensions of Kummer’s relations for ${}_2{}^{}F_1^{}$’s given in §15.10(ii). … …

2: 13.8 Asymptotic Approximations for Large Parameters

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§13.8(ii) Large $b$ and $z$, Fixed $a$ and $b/z$

… ►For the parabolic cylinder function $U$ see §12.2, and for an extension to an asymptotic expansion see Temme (1978). … ►

§13.8(iii) Large $a$

… ►For an extension to an asymptotic expansion complete with error bounds see Temme (1990b), and for related results see §13.21(i). … ► …

3: Bibliography C

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Table of integrals of squared Jacobian elliptic functions and reductions of related hypergeometric $R$-functions. Math. Comp. 75 (255), pp. 1309–1318.

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External Links:

ISSN 0025-5718, Document, MathReview, ZentralBlatt

Referenced by:

§19.25(v), §19.29(i), §22.14(ii).

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Numerical integration of related Hankel transforms by quadrature and continued fraction expansion. Geophysics 48 (12), pp. 1671–1686.

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Notes:

Fortran code.

External Links:

ISSN 0098-3500, Document

Referenced by:

§10.77(ix).

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An extension of the method of steepest descents. Proc. Cambridge Philos. Soc. 53, pp. 599–611.

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External Links:

MathReview (P. Henrici), ZentralBlatt

Referenced by:

§2.4(v).

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An extension of a Kummer’s quadratic transformation formula with an application. Proc. Jangjeon Math. Soc. 16 (2), pp. 229–235.

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External Links:

ISSN 1598-7264, MathReview (Petr Blaschke), ZentralBlatt

Referenced by:

§16.6, §16.6.

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Performance evaluation of programs related to the real gamma function. ACM Trans. Math. Software 17 (1), pp. 46–54.

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External Links:

ISSN 0098-3500, Document, MathReview, ZentralBlatt

Referenced by:

§5.24(ii), §5.24(iii).

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4: Bibliography M

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Chebyshev expansions for modified Struve and related functions. Math. Comp. 60 (202), pp. 735–747.

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External Links:

ISSN 0025-5718, FullText, MathReview, ZentralBlatt

Referenced by:

2nd item.

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Recursion relations for the $3$-$j$ symbols. Nuclear Physics A 113 (1), pp. 215–220.

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External Links:

Document

Referenced by:

§34.3(iii).

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Evaluation of complex logarithms and related functions. SIAM J. Numer. Anal. 18 (4), pp. 744–750.

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ISSN 0036-1429, Document, MathReview (M. Brannigan), ZentralBlatt

Referenced by:

§4.45(ii).

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

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ISSN 0377-0427, Document, MathReview Entry, ZentralBlatt

Referenced by:

§16.6.

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Lattice Statistics. In Applied Combinatorial Mathematics, E. F. Beckenbach (Ed.), University of California Engineering and Physical Sciences Extension Series, pp. 96–143.

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Notes:

Reprinted by Robert E. Krieger Publishing Co. in 1981.

External Links:

ZentralBlatt

Referenced by:

§26.20.

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