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arXiv · 1112.4830

Askey--Wilson Integral and its Generalizations

Paweł J. Szabłowski
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Abstract

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 system of recurrences that if solved successfully gives a sequence of generalized AW densities with more and more parameters.

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Paweł J. Szabłowski. 2014-12-05. Askey--Wilson Integral and its Generalizations. https://arxiv.org/abs/1112.4830

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