Characterization of q-Dunkl Appell symmetric orthogonal q-polynomials

We introduce a q  -Dunkl operator T(θ,q)≔Hq+θH−1T(θ,q)≔Hq+θH−1 where Hq is the q  -derivative one and we determine all symmetric T(θ,q)T(θ,q)-Appell classical orthogonal q-polynomials. Up to a dilatation, the solution is a q2-analogue of generalized Hermite polynomials orthogonal with respect to the form H(μ,q2)H(μ,q2). Integral representation and discrete measure of H(μ,q2)H(μ,q2) are given for some values of parameters.