Diverse characterizations of Q-Dunkl classical orthogonal polynomials

Abstract

In this paper, we present four characterizations of q-Dunkl-classical orthogonal polynomials. The first one is a T θ , q -distributional equation of Pearson type fulfilled by its associated form, where T θ , q is the q-Dunkl operator. The second is a second order linear T θ , q -difference equation. The third is a first order linear T θ , q -difference equation with polynomial coefficients satisfied by the corresponding Stieltjes function. The fourth is the so-called structure relation fulfilled by q-Dunkl-classical polynomials. Moreover, we provide an example of a non-symmetric sequence of T θ , q -classical orthogonal polynomials.