Solution in the Case of an Arbitrary Group

In chapter 4, the analysis was based on specific derivations (a closure property in some sense) rendered possible by the finiteness of the order of the group. Hereafter, we shall obtain the complete solution when the order of the group of the random walk is arbitrary, i.e. possibly infinite. The main idea consists in the reduction to a factorization problem on a curve in the complex plane. Generally one comes up first with integral equations and, in a second step, with explicit integral forms by means of Weierstrass functions.