Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-26T18:16:47.133Z Has data issue: false hasContentIssue false
  • English
  • Français

Application of the E-operator to evaluate an infinite integral

Published online by Cambridge University Press:  24 October 2008

F. Singh
F. Singh
Affiliation:
Government Engineering College, Bilaspur M.P., India
Get access Rights & Permissions [Opens in a new window]

Extract

1. The object of this paper is to evaluate an infinite integral, involving the product of H-functions, generalized hypergeometric functions and confluent hypergeometric functions by means of finite difference operators E. As the generalized hypergeometric function and H-function are of a very general nature, the integral, on specializing the parameters, leads to a generalization of many results some of which are known and others are believed to be new.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 65 , Issue 3 , May 1969 , pp. 725 - 730
Copyright
Copyright © Cambridge Philosophical Society 1969

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)Bajpai, S. D. Some integrals involving confluent hypergeometric functions and Meijer's G-functions, to appear in Math. Japon.Google Scholar
(2)Bateman Project. Tables of integral transforms, vol. I (MacGraw-Hill, 1954).Google Scholar
(3)Bateman Project. Higher transcendental functions, vol. I (MacGraw-Hill, 1953).Google Scholar
(4)Bbaaksma, B. L. J.Asymptotic expansions and analytic continuations for a class of Barnesintegral. Compositio Math. 15 (1963), 239–341.Google Scholar
(5)Cabslaw, H. S.Introduction to the theory of Fourier's series and integrals (Dover, 3rd revised edition).Google Scholar
(6)Fox, C.The G and H functions as symmetrical Fourier kernels. Trans. Amer. Math. Soc. 98 (1961), 395–429.Google Scholar
(7)Milne-Thomson, L. M.The calculus of finite differences (Macmillan, London 1933).Google Scholar
(8)Shabma, O. P.Certain infinite and finite integrals involving H-function and confluent hypergeometric functions. Proc. Nat. Acad. Sci., India, sect. A 36 (1966), 1023–1032.Google Scholar
(9)Rainvtlle, E. D.Special functions (Macmillan, New York 1965).Google Scholar