Diverse characterizations of Q-Dunkl classical orthogonal polynomials

In this paper, we present four characterizations of q-Dunkl-classical orthogonal polynomials. The first one is a Tθ,q-distributional equation of Pearson type fulfilled by its associated form, where Tθ,q is the q-Dunkl operator. The second is a second order linear Tθ,q-difference equation. The third is a first order linear Tθ,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 Tθ,q-classical orthogonal polynomials.