We consider a Mellin convolution integral representation of the second and third Appell's function and
apply an asymptotic method designed for this kind of integrals to derive new asymptotic expansions of the
Appell's functions F2 and F3 for one large variable. For certain values of the parameters, some of these
expansions involve logarithmic terms in the asymptotic variables. The results are illustrated with numerical
experiments.
** This is a joint work with: C. Ferreira, J. L. López.