New series representations for the two-loop massive sunset diagram

We derive new convergent series representations for the two-loop sunset diagram with three different propagator masses $$m_1,\, m_2$$m1,m2 and $$m_3$$m3 and external momentum p by techniques of analytic continuation on a well-known triple series that corresponds to the Lauricella $$F_C^{(3)}$$FC(3) 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 for the Lauricella series could be used in other settings as well.