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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
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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

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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
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(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