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Short communications

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

V. F. Tarasov

Bryansk State Technical University

Abstract: The Cauchy integral (3) for the representation of $\Gamma(z)$, when $\operatorname{Re}z<0$ 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.

UDC: 517.58+517.537.38

Received: 01.05.1996

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