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On the H -function

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  • Anatoly A. Kilbas
  • Megumi Saigo

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.

Suggested Citation

  • Anatoly A. Kilbas & Megumi Saigo, 1999. "On the H -function," International Journal of Stochastic Analysis, Hindawi, vol. 12, pages 1-14, January.
    • Handle: RePEc:hin:jnijsa:529827
    DOI: 10.1155/S1048953399000192
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