Hypergeometric solutions for the \(q\)-Painlevé equation of type \({E^{(1)}_6}\) by the Padé method (Q360399)
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scientific article; zbMATH DE number 6201610
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Hypergeometric solutions for the \(q\)-Painlevé equation of type \({E^{(1)}_6}\) by the Padé method |
scientific article; zbMATH DE number 6201610 |
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Hypergeometric solutions for the \(q\)-Painlevé equation of type \({E^{(1)}_6}\) by the Padé method (English)
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26 August 2013
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This work is related to Sakai's classification of discrete Painlevé equations through the geometry of rational surfaces. The particular cases of \(D_5^{(1)}\) and \(E_6^{(1)}\) are tackled. The Padé method is used to derive the latter equation; also solutions are obtained through a determinant formula, and a relation is given with Bäcklund transformations.
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hypergeometric solutions
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\(q\)-Painlevé equations
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Padé method
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QRT system
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Bäcklund transformation
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discrete Painlevé equation
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determinant formula
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0.8993869
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