Journal of Applied Mathematics and Stochastic Analysis
Volume 12 (1999), Issue 2, Pages 191-204
On the -function
1Belarusian State University, Department of Mathematics and Mechanics, Minsk 220050, Belarus
2Fukuoka University, Department of Applied Mathematics, Fukuoka 814-0180, Japan
Received 1 April 1997; Revised 1 September 1998
Copyright © 1999 Anatoly A. Kilbas and Megumi Saigo. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
This paper is devoted to the study of the -function as defined by the
where the function is a certain ratio of products of the Gamma-functions with the argument and the contour specially chosen. The
conditions for the existence of are discussed and explicit power
and power-logarithmic series expansions of near zero and infinity
are given. The obtained results define more precisely the known results.