Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Expansions of hypergeometric functions in hypergeometric functions

Authors: Jerry L. Fields and Jet Wimp
Journal: Math. Comp. 15 (1961), 390-395
MSC: Primary 33.20
MathSciNet review: 0125992
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] Y. L. Luke, ``Expansion of the confluent hypergeometric function in series of Bessel functions,'' MTAC, v. 13, 1959, p. 261-271. MR 0107027 (21:5754)
  • [2] A. Erdélyi, W. Magnus, F. Oberhettinger & F. G. Tricomi, Higher Transcendental Functions, McGraw-Hill Book Company, Inc., 1953, Vol. 1. Hereafter in this list, we use the abbreviation H.T.F.
  • [3] Y. L. Luke & Richard L. Coleman, ``Expansion of hypergeometric functions in series of other hypergeometric functions,'' Math. Comp., v. 15, 1961, p. 233. MR 0123745 (23:A1067)
  • [4] A. Erdélyi, W. Magnus, F. Oberhettinger & F. G. Tricomi, Tables of Integral Transforms, Vol. 1, McGraw-Hill Book Company, Inc., 1954.
  • [5] E. D. Rainville, ``Certain generating functions and their associated polynomials,'' Amer. Math. Monthly, v. 52, No. 5, May 1945, or H.T.F., Vol. 3, p. 239-250. MR 0011751 (6:211e)
  • [6] T. W. Chaundy, ``An extension of hypergeometric functions,'' Quart. J. Math. Oxford Ser. 14, 1943, p. 55-78. MR 0010749 (6:64d)
  • [7] C. S. Meijer, ``Expansion theorems for the G-function,'' Indag. Math., v. 14-17, 1952-55.
  • [8] H.T.F., Vol. 2.
  • [9] 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.
  • [10] G. N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge University Press, 1945. MR 1349110 (96i:33010)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 33.20

Retrieve articles in all journals with MSC: 33.20

Additional Information

Article copyright: © Copyright 1961 American Mathematical Society

American Mathematical Society