On the H-function. (1999) - Kilbas, Anatoly A.; Saigo, Megumi
Abstract : This paper is devoted to the study of the H -function as defined by the Mellin-Barnes integral H p, q m, n ( z ) = 1 2 π i ∫ ℒ ℋ p, q m, n ( s ) z − s d s, where the function ℋ p, q m, 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 H p, q m, n ( z ) are discussed and explicit power and power-logarithmic series expansions of H p, q m, n ( z ) near zero and infinity are given. The obtained results define more precisely the known results.