General solutions of second-order linear difference equations of Euler type

Abstract

The purpose of this paper is to give general solutions of linear difference equations which are related to the Euler-Cauchy differential equation \(y^{\prime\prime}+(\lambda/t^2)y=0\) or more general linear differential equations. We also show that the asymptotic behavior of solutions of the linear difference equations are similar to solutions of the linear differential equations.

Keywords

• Euler-Cauchy equations
• oscillation
• conditionally oscillatory