Some invariants for \(k\)th-order Lyness equation. (Q1767204)
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scientific article; zbMATH DE number 2140802
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Some invariants for \(k\)th-order Lyness equation. |
scientific article; zbMATH DE number 2140802 |
Statements
Some invariants for \(k\)th-order Lyness equation. (English)
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7 March 2005
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Second and third invariants are established for the \(k\)-th order Lyness equation \[ x_{n+1}=\frac{a+x_n+x_{n-1}+\cdots+x_{n-k+2}}{x_{n-k+1}},\quad n=0,1,2,\dots, \] where the parameter \(a\) is an arbitrary positive number. Furthermore, the independence of the second and third invariants are proved.
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Lyness equation
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invariants
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functionally independent invariants
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