Boundary value problems for some important classes of recurrent relations with two independent variables

Abstract

It is shown that complex-valued boundary value problems for several classes of recurrent relations with two independent variables, of some considerable interest, are solvable on the following domain: C = ((n,k): 0 ≤ k ≤ n,k E(open) N0, n E(open) Ng), the so called combinatorial domain. The recurrent relations include some of the most important combinatorial ones, which, among other things, serve as a motivation for the investigation. The methods for solving the boundary value problems are presented and explained in detail.