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P. B. Borwein, A. Cuyt, P. Zhou, Explicit Construction of General Multivariate Padé Approximant to an Appell function. Adv. Comput. Math. 2005. V. 22, N◦ 3.- P. 249-273.

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Article

A New Padé Approximant for the Appell Hypergeometric Function F1

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


Turkish Journal of Analysis and Number Theory. 2017, Vol. 5 No. 1, 13-17
DOI: 10.12691/tjant-5-1-3
Copyright © 2016 Science and Education Publishing

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.

Correspondence to: Abdallah  Hammam, Département de Mathématiques et Informatique, Faculté des sciences, Université Moulay Ismaïl, 50020 Meknès, Morocco. Email: a.hammam@fs.umi.ac.ma

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.

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