On The Solution of an Infinite System of Discrete Equations

Year 2020, Volume: 12 Issue: 2, 157 - 160, 31.12.2020

Anar Adiloğlu Mehmet Gürdal

https://doi.org/10.47000/tjmcs.822830

Cited By: 1

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.

Keywords

Difference equation, Jacobi matrix, Transformation operators, Direct problem, Inverse problem

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