  In 1944 Lars Onsager published the exact partition function of the
ferromagnetic Ising model on the infinite square lattice in terms of a definite
integral. Only in the literature of the last decade, however, has it been
recast in terms of special functions. Until now all known formulas for the
partition function in terms of special functions have been restricted to the
important special case of the isotropic Ising model with symmetric couplings.
Indeed, the anisotropic model is more challenging because there are two
couplings and hence two reduced temperatures, one for each of the two axes of
the square lattice. Hence, standard special functions of one variable are
inadequate to the task. Here, we reformulate the partition function of the
anisotropic Ising model in terms of the Kamp\'e de F\'eriet function, which is
a double hypergeometric function in two variables that is more general than the
Appell hypergeometric functions. Finally, we present hypergeometric formulas
for the generating function of multipolygons of given length on the infinite
square lattice, for isotropic as well as anisotropic edge weights. For the
isotropic case, the results allow easy calculation, to arbitrary order, of the
celebrated series first found by Cyril Domb.
