Science and Education Publishing Turkish Journal of Analysis and Number Theory 2333-1232 5 1 2016 12 26 A New Padé Approximant for the Appell Hypergeometric Function F1 13 17 EN Abdallah Hammam Département de Mathématiques et Informatique, Faculté des sciences, Université Moulay Ismaïl, 50020 Meknès, Morocco TJANT2017513 10.12691/tjant-5-1-3 2016 8 3 2016 11 15 2016 12 24 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.