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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 ∈  N 0  , n ∈ N }    , 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

Boundary Value Problems for Some Important Classes of Recurrent Relations with Two Independent Variables