Recurrent relations for the solutions of an infinite system of linear algebraic equations

Abstract

We obtain recurrent relations for bounded solutions of the system of equations

$$X_k - \sum\limits_{n = 0}^\infty {\frac{{(k + n)!}}{{k!n!}}} \alpha ^{k + n + 1} x_n = f_{k,} k = 0,1,..., \alpha \in (0,1/2),$$

with right-hand sides {f _k } ^∞ _k=0 ={δ _kj } ^∞ _k=0 ,j=0,1,..., where δ _kj is the Kronecker symbol.