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On the Mellin transform of a product of hypergeometric functions

Published online by Cambridge University Press:  17 February 2009

Allen R. Miller  and
H. M. Srivastava
Allen R. Miller
Affiliation:
1616 Eighteenth Street NW, Washington, D. C. 20009–2530, USA
H. M. Srivastava
Affiliation:
Department of Mathematics and Statistics, University of Victoria, Victoria, B. C. V8W 3P4, Canada.
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Abstract

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We obtain representations for the Mellin transform of the product of generalized hypergeometric functions0F1[−a2x2]1F2[−b2x2]fora, b > 0. The later transform is a generalization of the discontinuous integral of Weber and Schafheitlin; in addition to reducing to other known integrals (for example, integrals involving products of powers, Bessel and Lommel functions), it contains numerous integrals of interest that are not readily available in the mathematical literature. As a by-product of the present investigation, we deduce the second fundamental relation for3F2[1]. Furthermore, we give the sine and cosine transforms of1F2[−b2x2].

Type
Research Article
Information
The ANZIAM Journal , Volume 40 , Issue 2 , October 1998 , pp. 222 - 237
Copyright
Copyright © Australian Mathematical Society 1998

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