A duality of MacDonald-Koornwinder polynomials and its application to integral representations
type: Item
instance of: scholarly article
title: A duality of MacDonald-Koornwinder polynomials and its application to integral representations
zbMATH Open document ID: 1012.33018
DOI: 10.1215/S0012-7094-01-10723-0
author: Katsuhisa Mimachi
published in: Duke Mathematical Journal
publication date: 2002-10-27T00:00:00Z
review text: 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.
reviewed by: Angela Pasquale
Mathematics Subject Classification ID: 33D52
Mathematics Subject Classification ID: 33C70
zbMATH DE Number: 1820802
zbMATH Keywords: Koornwinder-Macdonald polynomials
zbMATH Keywords: Macdonald polynomials
zbMATH Keywords: Heckman-Opdam's Jacobi polynomials of \(BC_n\) type
zbMATH Keywords: duality formula
zbMATH Keywords: integral representations
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1820802