A New Padé Approximant for the Appell Hypergeometric Function F1

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 Pade 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.