Expansions of hypergeometric functions in hypergeometric functions

Fields, Jerry L.; Wimp, Jet

doi:10.1090/S0025-5718-1961-0125992-3

Expansions of hypergeometric functions in hypergeometric functions
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by Jerry L. Fields and Jet Wimp PDF

Math. Comp. 15 (1961), 390-395 Request permission

Abstract:

In [1] Luke gave an expansion of the confluent hypergeometric function in terms of the modified Bessel functions ${I_v}(z)$. The existence of other, similar expansions implied that more general expansions might exist. Such was the case. Here multiplication type expansions of low-order hypergeometric functions in terms of other hypergeometric functions are generalized by Laplace transform techniques.

References

Yudell L. Luke, Expansion of the confluent hypergeometric function in series of Bessel functions, Math. Tables Aids Comput. 13 (1959), 261–271. MR 107027, DOI 10.1090/S0025-5718-1959-0107027-2

Higher Transcendental Functions

H.T.F.

Yudell L. Luke and Richard L. Coleman, Expansion of hypergeometric functions in series of other hypergeometric functions, Math. Comp. 15 (1961), 233–237. MR 123745, DOI 10.1090/S0025-5718-1961-0123745-3

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T. W. Chaundy, An extension of hypergeometric functions. I, Quart. J. Math. Oxford Ser. 14 (1943), 55–78. MR 10749, DOI 10.1093/qmath/os-14.1.55

Indag. Math.

G. N. Watson, A treatise on the theory of Bessel functions, Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1995. Reprint of the second (1944) edition. MR 1349110