## Expansions of hypergeometric functions in hypergeometric functions

HTML articles powered by AMS MathViewer

- 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
A. Erdélyi, W. Magnus, F. Oberhettinger & F. G. Tricomi, - 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
A. Erdélyi, W. Magnus, F. Oberhettinger & F. G. Tricomi, - E. D. Rainville,
*Certain generating functions and associated polynomials*, Amer. Math. Monthly**52**(1945), 239–250. MR**11751**, DOI 10.2307/2305876 - 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
C. S. Meijer, “Expansion theorems for the G-function,” - 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**

*Higher Transcendental Functions*, McGraw-Hill Book Company, Inc., 1953, Vol. 1. Hereafter in this list, we use the abbreviation

*H.T.F.*

*Tables of Integral Transforms*, Vol. 1, McGraw-Hill Book Company, Inc., 1954.

*Indag. Math.*, v. 14-17, 1952-55. H.T.F., Vol. 2. J. L. Fields & Y. L. Luke, “Asymptotic expansions of a class of hypergeometric polynomials with respect to the order,” Midwest Research Institute Technical Report, July 1, 1959.

## Additional Information

- © Copyright 1961 American Mathematical Society
- Journal: Math. Comp.
**15**(1961), 390-395 - MSC: Primary 33.20
- DOI: https://doi.org/10.1090/S0025-5718-1961-0125992-3
- MathSciNet review: 0125992