
Journal of the Australian Mathematical Society  Series B
Vol. 40 Part 2 (1998)
On the Mellin transform of a product of hypergeometric functions
Allen R. Miller
1616 Eighteenth Street NW
Washington, D. C. 200092530
USA
and
H. M. Srivastava
Department of Mathematics
and Statistics
University of Victoria
Victoria, B. C. V8W 3P4
Canada.
Abstract:
We obtain representations for the Mellin transform of the product of
generalized hypergeometric functions
_{0}F_{1}[a^{2}x^{2}]_{1}F_{2}[b^{2}x^{2}] for
a,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 byproduct of the
present investigation, we deduce the second fundamental relation for
_{3}F_{2}[1]. Furthermore, we give the sine and cosine transforms of
_{1}F_{2}[b^{2}x^{2}].
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