On the solutions of second order difference equations with variable coefficients
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Date
2024
Authors
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Journal ISSN
Volume Title
Publisher
faculty of engineering and natural sciences
Abstract
In this article, we explore solutions to second-order linear difference equations featuring variable coefficients. By imposing mild conditions, we present closed-form solutions through the utilization of finite continued fraction representations. The proof of our results relies on elementary techniques, specifically involving factoring a quadratic shift operator. As a consequential application, we unveil two novel generalized continued fraction formulas for the mathematical constant π 2 .
Description
Keywords
Difference equations, continued fraction, non-homogeneous equations
Citation
Shynarbekb N , Shynarbekb N. , Orynbassar A , On the solutions of second order difference equations with variable coefficients / Mathematics and Science Education / 2024