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An integral involving the G-function and Kampé de Fériet function

Published online by Cambridge University Press:  24 October 2008

O Shanker
O Shanker
Affiliation:
Punjabi University, Patiala, India
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Extract

The object of this paper is to evaluate an infinite integral involving the product of Meijer's G-function (5) and Kampé de Fériet function (1) in terms of Kampé de Fériet function. A number of papers of Bailey (3,4), Ragab (7,8), Slater (9), and Srivastava (10) have appeared, evaluating an integral in terms of a hypergeometric function of two variables or in terms of an E-function. Their results are obviously the particular cases of my result. Since Meijer's G-function is the most general function of one variable which can be expressed in terms of special functions (5) and Kampé de Fériet's function being the most general hypergeometric function of two variables, the integral given by me is the most general integral ever obtained and generalizes most of the results obtained so far for the integral of Mellin type in terms of generalized hypergeometric series. This is because the Kampé de Fériet function reduces to the product of two generalized hypergeometric functions by choosing parameters suitably.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 64 , Issue 4 , October 1968 , pp. 1041 - 1044
Copyright
Copyright © Cambridge Philosophical Society 1968

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References

REFERENCES

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