We give a formula representing a duality of Macdonald-Koornwinder polynomials. Using this formula, an integral representation of Macdonald-Koornwinder polynomials is derived, a special case of which is the conjectural formula stated in . We also present the corresponding formula to Heckman and Opdam's Jacobi polynomials of type $BC_m$.
"A duality of MacDonald-Koornwinder polynomials and its application to integral representations." Duke Math. J. 107 (2) 265 - 281, 1 April 2001. https://doi.org/10.1215/S0012-7094-01-10723-0