A duality of MacDonald-Koornwinder polynomials and its application to integral representations (Q1847821)
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scientific article; zbMATH DE number 1820802
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A duality of MacDonald-Koornwinder polynomials and its application to integral representations |
scientific article; zbMATH DE number 1820802 |
Statements
A duality of MacDonald-Koornwinder polynomials and its application to integral representations (English)
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27 October 2002
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The Koornwinder-Macdonald polynomials form a general class of orthogonal polynomials containing as limiting cases several important families of orthogonal polynomials, such as the Macdonald polynomials for classical root systems, the multivariable Wilson polynomials and Heckman-Opdam's Jacobi polynomials of \(BC_n\) type. The main result of this paper is a duality formula satisfied by the Koornwinder-Macdonald polynomials. Using the orthogonality relations, the author deduces from it an integral representation for the Koornwinder-Macdonald polynomials. The duality formula and integral representation are also presented in the limiting case of Heckman-Opdam polynomials of \(BC_n\) type.
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Koornwinder-Macdonald polynomials
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Macdonald polynomials
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Heckman-Opdam's Jacobi polynomials of \(BC_n\) type
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duality formula
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integral representations
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