Hostname: page-component-8448b6f56d-dnltx Total loading time: 0 Render date: 2024-04-16T13:01:03.017Z Has data issue: false hasContentIssue false
  • English
  • Français

An integral involving the product of a G-function and a generalized hypergeometric function

Published online by Cambridge University Press:  24 October 2008

S. P. Chhabra  and
F. Singh
S. P. Chhabra
Affiliation:
Govt. Engineering College, Bilaspur, India
F. Singh
Affiliation:
Govt. Engineering College, Bilaspur, India
Get access Rights & Permissions [Opens in a new window]

Extract

1. In this note a definite integral involving the product of Meijer's G-function and a generalized hypergeometric function is evaluated with the help of finite difference operators E. As the generalized hypergeometric function and Meijer's G-function may be converted into a number of polynomials and higher transcendental functions, the integral leads to a generalization of many results. The results given by Agrawal ((l), integral 4), Sharma ((7), integral 1) in these proceedings, Bhonsle ((2), p. 188) and Saxena ((6), p. 198) follow as particular cases of our formula. In what follows v, μ, m and h are positive integers and either of v and μ may be zero. The symbol Δ(m, a) denotes a set of m parameters a/m, (a + 1 )/m, …, (a + m − 1 )/m.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 65 , Issue 2 , March 1969 , pp. 479 - 482
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)Agrawal, B. M.Application of Δ and E operators to evaluate certain integrals. Proc. Cambridge Philos. Soc. 63 (1967), 99.Google Scholar
(2)Bhonsle, B. R.Some results involving Jacobi polynomials. J. Indian Math. Soc. 26 (1962) 187–190.Google Scholar
(3)Carslaw, H. S.Introduction to the theory of Fouriers' series and integrals (Dover, 3rd revised edition).Google Scholar
(4)Erdelyi, A. et al. Higher transcendental functions, vol. i (McGraw-Hill; New York, 1953).Google Scholar
(5)Milne-Thompson, L. M.The calculus of finite differences (1938).Google Scholar
(6)Saxena, R. K.On some results involving Jacobi polynomials J. Indian Math. Soc. 28 (1964), 197–202.Google Scholar
(7)Sharma, K. C.Integrals involving products of G-function and Gauss's hypergeometric function. Proc. Cambridge Philos. Soc. 60 (1964), 539–542.CrossRefGoogle Scholar