Closed-form solution of a rational difference equation $x_{n+1}=\frac{x_{n-(9 t+8)}}{1+\prod_{k=0}^{6} x_{n-(t+1) k-t} }

Prof. Mohamed Abd El-Moneam; N. A.   Askar; B. S. Alamri B. S. Alamri

doi:10.22541/au.165604685.59959905/v1

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Closed-form solution of a rational difference equation $x_{n+1}=\frac{x_{n-(9 t+8)}}{1+\prod_{k=0}^{6} x_{n-(t+1) k-t} }

Prof. Mohamed Abd El-Moneam,
N. A. Askar,
B. S. Alamri B. S. Alamri

Abstract

In this paper, we obtain the solutions of the difference equation \begin{equation*} x_{n+1}=\frac{x_{n-(9 t+8)}}{1+\prod_{k=0}^{6} x_{n-(t+1) k-t}}, \end{equation*} where the initials are positive real numbers.