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
Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026