q-Selberg Integrals and Koornwinder Polynomials
Copyright policy )q-Selberg Integrals and Koornwinder Polynomials
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.
Mehta's integral, quadratic norm formula, antisymmetrization, 33D52, 05A30, 11B65, Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.), Binomial coefficients; factorials; \(q\)-identities, Mathematics - Classical Analysis and ODEs, \(q\)-calculus and related topics, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Mathematics - Combinatorics, \(q\)-Selberg integral, Combinatorics (math.CO), Koornwinder polynomials
Mehta's integral, quadratic norm formula, antisymmetrization, 33D52, 05A30, 11B65, Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.), Binomial coefficients; factorials; \(q\)-identities, Mathematics - Classical Analysis and ODEs, \(q\)-calculus and related topics, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Mathematics - Combinatorics, \(q\)-Selberg integral, Combinatorics (math.CO), Koornwinder polynomials
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