On the solutions of second order difference equations with variable coefficients

Shirali Kadyrov; Alibek Orynbassar

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arXiv · 2103.03554

On the solutions of second order difference equations with variable coefficients

Shirali Kadyrov·Alibek Orynbassar

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Abstract

In this article we study solutions to second order linear difference equations with variable coefficients. Under mild conditions we provide closed form solutions using finite continued fraction representations. The proof of the results are elementary and based on factoring a quadratic shift operator. As an application, we obtain two new generalized continued fraction formulas for the mathematical constant $\pi^2$.

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Shirali Kadyrov, Alibek Orynbassar. 2021-03-05. On the solutions of second order difference equations with variable coefficients. https://arxiv.org/abs/2103.03554

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