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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
Prof. Mohamed Abd El-Moneam
Jazan University
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N. A. Askar
Mathematics Department, Faculty of Science, Jazan University, Kingdom of Saudi Arabia
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B. S. Alamri B. S. Alamri
Mathematics Department, Faculty of Science, Jazan University, Kingdom of Saudi Arabia.
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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.