Askey-Wilson integral and its generalizations
[摘要] We expand the Askey-Wilson (AW) density in a series of products of continuous q-Hermite polynomials times the density that makes these polynomials orthogonal. As a by-product we obtain the value of the AW integral as well as the values of integrals of q-Hermite polynomial times the AW density (q-Hermite moments of AW density). Our approach uses nice, old formulae of Carlitz and is general enough to venture a generalization. We prove that it is possible and pave the way how to do it. As a result, we obtain a system of recurrences that if solved successfully gives a sequence of generalized AW densities with more and more parameters. MSC: 33D45, 05A30, 05E05.
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[效力级别] [学科分类] 数学(综合)
[关键词] Askey-Wilson integral;Askey-Wilson polynomials;q-Hermite polynomials;expansion of ratio of densities;symmetric functions [时效性]