A duality of MacDonald-Koornwinder polynomials and its application to integral representations (Q1847821)

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.