On the recursive sequence \(x_{n+1}=\frac{x_{n-(5k+9)}}{1+x_{n-4}x_{n-9}\cdots x_{n-(5k+4)}}\) (Q2518172)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the recursive sequence \(x_{n+1}=\frac{x_{n-(5k+9)}}{1+x_{n-4}x_{n-9}\cdots x_{n-(5k+4)}}\) |
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On the recursive sequence \(x_{n+1}=\frac{x_{n-(5k+9)}}{1+x_{n-4}x_{n-9}\cdots x_{n-(5k+4)}}\) (English)
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15 January 2009
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The solutions with positive initial values of the difference equation in the title are investigated with respect to periodicity resp. convergence. Reviewer's remark: At least 80\% of the paper is redundant, since the results follow easily from corresponding ones regarding the simpler equation \(x_n=x_{n-k}/(1+x_{n-1}\cdots x_{n-k+1})\).
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rational difference equation
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periodicity
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convergence
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