  A representation of the two-loop contribution to the pion decay constant in
$SU(3)$ chiral perturbation theory is presented. The result is analytic upto
the contribution of the three (different) mass sunset integrals, for which an
expansion in their external momentum has been taken. We also give an analytic
expression for the two-loop contribution to the pion mass based on a
renormalized representation and in terms of the physical eta mass. We find an
expansion of $F_{\pi}$ and $M_{\pi}^2$ in the strange quark mass in the isospin
limit, and perform the matching of the chiral SU(2) and SU(3) low energy
constants. A numerical analysis demonstrates the high accuracy of our
representation, and the strong dependence of the pion decay constant upon the
values of the low energy constants, especially in the chiral limit. Finally, we
present a simplified representation that is particularly suitable for fitting
with available lattice data.
