On the solutions of second order difference equations with variable coefficients


Kadyrov S. Shynarbek N. Orynbassar A.
Jun 2025Taru Publications

Journal of Interdisciplinary Mathematics
2025#28Issue 41517 - 1527 pp.

In this article, we explore solutions to second-order linear difference equations featuring variable coefficients. By imposing mild conditions, we present closed-form solutions by utilizing 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 π2.

Apéry-like series , Closed form solutions , Continued fractions , Difference equations , Non-homogeneous equations , π

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Department of General Education, New Uzbekistan University, Tashkent, Uzbekistan
Pedagogy of Natural Sciences, Suleyman Demirel University, 1/1 Abylay Khan, Kaskelen, Kazakhstan

Department of General Education
Pedagogy of Natural Sciences

10 лет помогаем публиковать статьи Международный издатель

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