Askey-Wilson integral and its generalizations

Advances in Difference Equations

Pawe J Szabowski¹ 

[1] Department of Mathematics and Information Sciences, Warsaw University of Technology, Warsaw, Poland

关键词: Askey-Wilson integral;    Askey-Wilson polynomials;    q-Hermite polynomials;    expansion of ratio of densities;    symmetric functions;   

DOI  :  10.1186/1687-1847-2014-316

学科分类：数学（综合）

来源: SpringerOpen

【 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.

【 授权许可】

CC BY