Treffer: A duality of MacDonald-Koornwinder polynomials and its application to integral representations
Title:
A duality of MacDonald-Koornwinder polynomials and its application to integral representations
Authors:
Source:
Duke Math. J. 107, no. 2 (2001), 265-281
Publisher Information:
Duke University Press, 2001.
Publication Year:
2001
Subject Terms:
Other hypergeometric functions and integrals in several variables, duality formula, Koornwinder-Macdonald polynomials, 33C70, integral representations, Macdonald polynomials, 0101 mathematics, 33D52, Heckman-Opdam's Jacobi polynomials of \(BC_n\) type, 01 natural sciences, Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.)
Document Type:
Fachzeitschrift
Article<br />Other literature type
File Description:
application/xml; application/pdf
ISSN:
0012-7094
DOI:
10.1215/s0012-7094-01-10723-0
Access URL:
https://zbmath.org/1820802
https://doi.org/10.1215/s0012-7094-01-10723-0
https://projecteuclid.org/journals/duke-mathematical-journal/volume-107/issue-2/A-duality-of-MacDonald-Koornwinder-polynomials-and-its-application-to/10.1215/S0012-7094-01-10723-0.full
https://projecteuclid.org/euclid.dmj/1091736758
https://doi.org/10.1215/s0012-7094-01-10723-0
https://projecteuclid.org/journals/duke-mathematical-journal/volume-107/issue-2/A-duality-of-MacDonald-Koornwinder-polynomials-and-its-application-to/10.1215/S0012-7094-01-10723-0.full
https://projecteuclid.org/euclid.dmj/1091736758
Accession Number:
edsair.doi.dedup.....828a469edd14fba1350791805a3329cc
Database:
OpenAIRE
Weitere Informationen
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.