On the H-function. (1999)

• Record Type: Journal Article
• Authors: Kilbas, Anatoly A.; Saigo, Megumi
• Is Part Of: Journal of applied mathematics and stochastic analysis. Volume 12:Number 2(1999)
• Page Start: 191
• Page End: 204
• Publication Date: 1999
• Subjects: H-function; Mathematical models -- Periodicals; Computer simulation -- Periodicals; Computer science -- Mathematics -- Periodicals; Computer science -- Mathematics; Computer simulation; Mathematical models; Applied Mathematics; Periodicals; Electronic journals; 519.22
• DOI: 10.1155/S1048953399000192
• Languages: English
• ISSNs: 1048-9533

Abstract

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.