On The Solution of an Infinite System of Discrete Equations

Abstract

In this work, we construct the transformation operator for the infinite system of the difference equations $a_{n-2}y_{n-2}+b_{n-1}y_{n-1}+c_{n}y_{n}+b_{n}y_{n+1}+a_{n}y_{n+2}=\lambda y_{n}$ $(n=1,2,...)$,where $a_{n}\neq0,$ $b_{n},$ $c_{n}$ $(n=1,2,3,...)$ are given complex numbers, investigate some important properties of the special solutions of the difference system.