Resumen de Asymptotic expansions of the Appell's function F2

José Luis López García , María Esther García

• The second Appell¿s hypergeometric function F2(a,b,b0,c,c0; x,y) is considered for large values of its variables x and y. An integral representation of F2 is obtained in the form of a double integral. This integral is a two-dimensional generalization of the typical one-dimensional integral to which the analytic continuation method of asymptotic expansions of integrals may be applied. We show that the analytic continuation method can also be applied to this kind of two-dimensional integrals. Then, we derive an asymptotic expansion of F2(a,b,b0,c,c0; x,y) in decreasing powers of x and y. Coefficients of the expansion are given in terms of the hypergeometric function 3F2. As numerical experiments show, the approximation is considerable accurate