Characterization of q-Dunkl Appell symmetric orthogonal q-polynomials

Abstract

We introduce a q-Dunkl operator T ( θ , q ) ≔ H q + θ H − 1 where H q is the q-derivative one and we determine all symmetric T ( θ , q ) -Appell classical orthogonal q-polynomials. Up to a dilatation, the solution is a q 2-analogue of generalized Hermite polynomials orthogonal with respect to the form H ( μ , q 2 ) . Integral representation and discrete measure of H ( μ , q 2 ) are given for some values of parameters.