Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-25T13:44:02.508Z Has data issue: false hasContentIssue false
  • English
  • Français

A hypergeometric transformation associated with the Appell function F4

Published online by Cambridge University Press:  24 October 2008

H. M. Srivastava
H. M. Srivastava
Affiliation:
Department of Mathematics, Jodhpur University, India
Get access Rights & Permissions [Opens in a new window]

Extract

Recently in these proceedings (see (5), p. 175) by applying Goldstein's form of Parseval's relation ((4), p. 105) to the operational pairs ((3), p. 284)

where R[(b ± c)2] > 0 and ((3), p. 293)

where R(½ − λ + μ) > 0, it was proved that if

then

provided R(½ − λ + μ + ν) > 0 and R[(b ± c)2] > R(a), 0.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 62 , Issue 4 , October 1966 , pp. 765 - 767
Copyright
Copyright © Cambridge Philosophical Society 1966

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Appell, P. et Kampé De Fériet, J.Fonctions hypergéométriques et hypersphériques: Polynomes d'hermite (Gauthier-Villars; Paris, 1926).Google Scholar
(2)Eedélyi, A.Transformations of hypergeometric functions of two variables. Proc. Roy. Soc. Edinburgh. Sec. A 62 (1948), 378–385.Google Scholar
(3)Erdélyi, A., Magnus, W., Oberhettinger, F. and Tricomi, F. G.Tables of integral transforms, vol. I (McGraw-Hill; New York, 1954).Google Scholar
(4)Goldstein, S.Operational representation of Whittaker's confluent hypergeometric function and Weber's parabolic cylinder function. Proc. London Math. Soc. (2) 34 (1932), 103–125.CrossRefGoogle Scholar
(5)Saxena, R. K.Integrals involving Bessel functions and Whittaker functions. Proc. Cambridge Philos. Soc. 60 (1964), 174–176.CrossRefGoogle Scholar
(6)Slater, L. J.Confluent hypergeometric functions (Cambridge, 1960).Google Scholar