Journal of Applied Mathematics and Stochastic Analysis
Volume 12 (1999), Issue 2, Pages 191-204
doi:10.1155/S1048953399000192

On the H-function

Anatoly A. Kilbas1 and Megumi Saigo2

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.

Abstract

This paper is devoted to the study of the H-function as defined by the Mellin-Barnes integral Hp,qm,n(z)=12πi∫ℒℋp,qm,n(s)z−sds, where the function ℋp,qm,n(s) is a certain ratio of products of the Gamma-functions with the argument s and the contour ℒ specially chosen. The conditions for the existence of Hp,qm,n(z) are discussed and explicit power and power-logarithmic series expansions of Hp,qm,n(z) near zero and infinity are given. The obtained results define more precisely the known results.