Turkish Journal of Analysis and Number Theory
ISSN (Print): 2333-1100 ISSN (Online): 2333-1232 Website: http://www.sciepub.com/journal/tjant
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Turkish Journal of Analysis and Number Theory. 2017, 5(1), 13-17
DOI: 10.12691/tjant-5-1-3
Open AccessArticle

A New Padé Approximant for the Appell Hypergeometric Function F1

Abdallah Hammam1,

1Département de Mathématiques et Informatique, Faculté des sciences, Université Moulay Ismaïl, 50020 Meknès, Morocco

Pub. Date: December 26, 2016

Cite this paper:
Abdallah Hammam. A New Padé Approximant for the Appell Hypergeometric Function F1. Turkish Journal of Analysis and Number Theory. 2017; 5(1):13-17. doi: 10.12691/tjant-5-1-3

Abstract

In this work, we present a simple method for computing the first Appell function F1(a,b,b’;c;x,y), in some particular case. We use a new definition of the general multivariate Padé approximant which allows us to get the explicit expression of the denominator polynomial. Our approach seems to give a better precision than the Taylor’s expansion, especially near the border of the convergence area.

Keywords:
hypergeometric functions multivariate approximation.

Creative CommonsThis work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

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