FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

1998, VOLUME 4, NUMBER 1, PAGES 467-470

The Cauchy--Mellin integral transformation for $\Gamma \; (z)$ and its application

V. F. Tarasov

Abstract

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The Cauchy integral (3) for the representation of $\Gamma \; (z)$, when is a noninteger, and the Mellin integral (4) together form the new "integral transformation of Cauchy--Mellin type" for $\Gamma \; (z)$, with the help of which we can find exact analytical representations in form of "nonorientable" power series for hypergeometric functions from one, two and more variables in a "pole-domain" of Euler's gamma-function.

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Last modified: April 8, 1998