Characterization of the Dunkl-classical symmetric orthogonal polynomials

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摘要

In this paper, we introduce the notion of Dunkl-classical orthogonal polynomials. Then, we show that generalized Hermite and generalized Gegenbauer polynomials are the only Dunkl-classical symmetric orthogonal polynomials by solving a suitable differential-difference equation.

论文关键词：Orthogonal polynomials,Symmetric orthogonal polynomials,Dunkl operator,Generalized Hermite polynomials,Generalized Gegenbauer polynomials,Sieved ultraspherical polynomials

论文评审过程：Available online 12 October 2006.

论文官网地址：https://doi.org/10.1016/j.amc.2006.08.108