$q$-Selberg Integrals and Koornwinder Polynomials

Symmetry Integrability and Geometry-Methods and Applications

article

Jyoichi Kaneko¹ 

[1] Department of Mathematical Sciences, University of the Ryukyus

关键词: Koornwinder polynomials;    quadratic norm formula;    antisymmetrization;    $q$-Selberg integral;    Mehta's integral.;   

DOI  :  10.3842/SIGMA.2022.014

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown