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

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.