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International mathematical journal of analysis and its applications

Editor-in-Chief: Schulz, Friedmar

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CiteScore 2017: 0.66

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Volume 36, Issue 1


The generalized hypergeometric function as the Meijer G-function

Anatoly A. Kilbas / Ram K. Saxena / Megumi Saigo / Juan J. Trujillo
  • Corresponding author
  • Departamento de Análisis Matemático, Universidad de La Laguna, La Laguna, Tenerife 38271, Spain
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Published Online: 2015-09-03 | DOI: https://doi.org/10.1515/anly-2015-5001


In this paper, we use the representation of the generalized hypergeometric function pFq in terms of the known Meijer G-function to extend the range of parameters of such a special function so it be convergent. Also, we establish the corresponding series representation for such an extension. In particular, we extend the hypergeometric functions 2F1 and 3F2 from |z|<1 to |z|>1. Moreover, we obtain asymptotic formulas to estimate the extended pFq at infinity.

Keywords: Generalized hypergeometric function; Mellin–Barnes integral; Meijer G-function; generalized hypergeometric series; Gauss hypergeometric function; series representations; asymptotic estimates

MSC: 33C60; 33C20; 33C05; 41A60

About the article

Received: 2014-07-05

Accepted: 2015-03-20

Published Online: 2015-09-03

Published in Print: 2016-02-01

Citation Information: Analysis, Volume 36, Issue 1, Pages 1–14, ISSN (Online) 2196-6753, ISSN (Print) 0174-4747, DOI: https://doi.org/10.1515/anly-2015-5001.

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