A New Padé Approximant for the Appell Hypergeometric Function F1

Abdallah Hammam^1,

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

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.

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