# Sturm-Liouville Difference Equations Having Special Potentials

## TL;DR

This paper introduces a novel approach to solving Sturm-Liouville difference equations with special potentials, providing solution representations, asymptotic formulas, and numerical eigenfunction comparisons to enhance spectral theory applications.

## Contribution

It offers new methods for analyzing Sturm-Liouville difference equations with specific potentials, including solution representations and asymptotic analysis.

## Key findings

- Derived solution representations and asymptotic formulas.
- Numerical comparisons of eigenfunctions.
- Applications demonstrating spectral theory relevance.

## Abstract

In this paper, we present a new approachment for Sturm-Liouville problem having special potentials. We acquire the representations of solutions and asymptotic formulas for solutions with regard to initial conditions. Also, a few applications are given to show the requirement of Sturm-Liouville difference equations having potential function in view of suitability to the spectral theory. The approximate numerical outcomes for the eigenfunctions are compared with each other.

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Source: https://tomesphere.com/paper/1703.10700