A generalization of a theorem of Bochner (Q1414306)
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scientific article; zbMATH DE number 2006400
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A generalization of a theorem of Bochner |
scientific article; zbMATH DE number 2006400 |
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A generalization of a theorem of Bochner (English)
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20 November 2003
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A theorem of \textit{S.~Bochner} [Über Sturm-Liouvillesche Polynomsysteme, Math. Z. 29, 730--736 (1929; JFM 55.0260.01)] for classifying polynomial solutions to a certain second order differential equation is generalized to the \(q\)-hypergeometric case. To this end, the ordinary differential operators are replaced by the Askey-Wilson divided difference operators. The solutions, which have been Jacobi, Laguerre, and Bessel polynomials in Bochner's case, then turn out to be variants of Askey-Wilson polynomials.
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Bochner's theorem
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orthogonal polynomials
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