q-Selberg Integrals and Koornwinder Polynomials

Jyoichi Kaneko, University of the Ryukyus, Japan
2022 Symmetry, Integrability and Geometry: Methods and Applications  
We prove a generalization of the q-Selberg integral evaluation formula. The integrand is that of q-Selberg integral multiplied by a factor of the same form with respect to part of the variables. The proof relies on the quadratic norm formula of Koornwinder polynomials. We also derive generalizations of Mehta's integral formula as limit cases of our integral.
doi:10.3842/sigma.2022.014 fatcat:64sytnrjjzdnnkogymjehba6ti