  We present the reduction of the correlation functions of the Ising model on
the anisotropic square lattice to complete elliptic integrals of the first,
second and third kind, the extension of Kramers-Wannier duality to anisotropic
correlation functions, and the linear differential equations for these
anisotropic correlations. More precisely, we show that the anisotropic
correlation functions are homogeneous polynomials of the complete elliptic
integrals of the first, second and third kind. We give the exact dual
transformation matching the correlation functions and the dual correlation
functions. We show that the linear differential operators annihilating the
general two-point correlation functions are factorised in a very simple way, in
operators of decreasing orders.
