  We derive new convergent series representations for the two-loop sunset
diagram with three different propagator masses m1, m2 and m3 and external
momentum p by techniques of analytic continuation on a well-known triple series
that corresponds to the Lauricella Fc function. The convergence regions of the
new series contain regions of interest to physical problems. These include some
ranges of masses and squared external momentum values which make them useful
from Chiral Perturbation Theory to some regions of the parameter space of the
Minimal Supersymmetric Standard Model. The analytic continuation results
presented on the Lauricella series could be used in other settings as well.
