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# Analysis

### International mathematical journal of analysis and its applications

Editor-in-Chief: Schulz, Friedmar

4 Issues per year

Cite Score 2016: 0.65

SCImago Journal Rank (SJR) 2016: 0.125
Source Normalized Impact per Paper (SNIP) 2016: 3.360

Mathematical Citation Quotient (MCQ) 2016: 0.34

Online
ISSN
2196-6753
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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

## Abstract

In this paper, we use the representation of the generalized hypergeometric function ${\phantom{\rule{0.166667em}{0ex}}}_{p}{F}_{q}$ 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 ${\phantom{\rule{0.166667em}{0ex}}}_{2}{F}_{1}$ and ${\phantom{\rule{0.166667em}{0ex}}}_{3}{F}_{2}$ from $|z|<1$ to $|z|>1$. Moreover, we obtain asymptotic formulas to estimate the extended ${\phantom{\rule{0.166667em}{0ex}}}_{p}{F}_{q}$ at infinity.

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

## About the article

Accepted: 2015-03-20

Published Online: 2015-09-03

Published in Print: 2016-02-01

Funding Source: Belarusian Fundamental Research Fund

Award identifier / Grant number: F03MC-008

Funding Source: Universidad de La Laguna

Funding Source: University Grants Commission of India

Citation Information: Analysis, Volume 36, Issue 1, Pages 1–14, ISSN (Online) 2196-6753, ISSN (Print) 0174-4747,

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© 2016 by De Gruyter.