A characterization of symmetric Tμ-classical monic orthogonal polynomials by a structure relation

Abstract

The aim of this work is to study the symmetric orthogonal polynomials’ sequences which are Dunkl-classical. We recover again that the generalized Hermite polynomials and the generalized Gegenbauer polynomials are the only symmetric Dunkl-classical through a different manner that in Ben Cheikh and Gaied [Characterization of the Dunkl-classical symmetric orthogonal polynomials. Appl Math Comput. 2007;187:105–114] by solving a differential-difference equation in the dual space of polynomials. Moreover, we deduce the structure relation that such a symmetric monic orthogonal polynomials satisfies.