eng Science and Education Publishing Turkish Journal of Analysis and Number Theory 2333-1232 2016-12-26 5 1 13 17 10.12691/tjant-5-1-3 TJANT2017513 article Abdallah Hammam a.hammam@fs.umi.ac.ma 1 Département de Mathématiques et Informatique, Faculté des sciences, Université Moulay Ismaïl, 50020 Meknès, Morocco 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. http://pubs.sciepub.com/tjant/5/1/3/tjant-5-1-3.pdf hypergeometric functions multivariate approximation