The third Appell function for one large variable

We consider the Mellin convolution integral representation of the third Appell function given in Erdélyi (1953) [8]. Then, we apply the asymptotic method designed in Wong (1979) [22] and revisited in López (2008) [14] for this kind of integral to derive new asymptotic expansions of the Appell function F3 for one large variable in terms of hypergeometric functions. The accuracy of the approximations is illustrated with numerical experiments.