FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

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

V. F. Tarasov

Abstract

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```
The Cauchy integral (3) for the representation of
```$\Gamma(z)$ ,
when $\Re z<0$
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.

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Last modified: April 8, 1998