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International Journal of Stochastic Analysis

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International Journal of Stochastic Analysis / 1999 / Article

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Volume 12 |Article ID 529827 | https://doi.org/10.1155/S1048953399000192

Anatoly A. Kilbas, Megumi Saigo, "On the H-function", International Journal of Stochastic Analysis, vol. 12, Article ID 529827, 14 pages, 1999. https://doi.org/10.1155/S1048953399000192

On the H-function

Anatoly A. Kilbas1 and Megumi Saigo2

1Belarusian State University, Department of Mathematics and Mechanics, Belarus

2Fukuoka University, Department of Applied Mathematics, Japan

Received01 Apr 1997
Revised01 Sep 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.

Copyright © 1999 Hindawi Publishing Corporation. 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.

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