The Second Appell Function for one Large Variable

We consider the Mellin convolution integral representation of the second Appell function given in 8]. Then, we apply the asymptotic method designed in 12] for this kind of integrals to derive new asymptotic expansions of the Appell function F ₂ for one large variable in terms of hypergeometric functions. For certain values of the parameters, some of these expansions involve logarithmic terms in the asymptotic variables. The accuracy of the approximations is illustrated with numerical experiments.