Shynarbekb N.Shynarbekb N.Orynbassar A.2025-08-132025-08-132024Shynarbekb N , Shynarbekb N. , Orynbassar A , On the solutions of second order difference equations with variable coefficients / Mathematics and Science Education / 2024https://repository.sdu.edu.kz/handle/123456789/1880In 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 .enDifference equationscontinued fractionnon-homogeneous equationsArticle