Special function solutions of the discrete Painlevé equations (Q1600404)
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scientific article; zbMATH DE number 1755277
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Special function solutions of the discrete Painlevé equations |
scientific article; zbMATH DE number 1755277 |
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Special function solutions of the discrete Painlevé equations (English)
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13 June 2002
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A review of special solutions of discrete (difference) and \(q\)-discrete Painlevé equations in terms of discrete special functions is given. It is shown that these solutions exist if the parameters of the Painlevé equation satisfy a particular constraint. The discrete special functions belong to the hypergeometric family, although in some cases they seem to go beyond the known discrete and \(q\)-discrete hypergeometric functions.
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Painlevé equation
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discrete special function
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affine Weyl groups
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