Characterizations of the Symmetric T(θ, q)-Classical Orthogonal q-Polynomials

In this paper, we give two characterizations for symmetric q-Dunkl-classical orthogonal polynomials. The first one is related to a spectral problem for a second-order linear q-difference differential operator. The second one is given by a distribution equation of Pearson type fulfilled by their corresponding linear functionals. Then, we show that the q(2)-analogue of generalized Hermite and the q(2)-analogue of generalized Gegenbauer polynomials are, up a dilation, the only symmetric q-Dunkl-classical orthogonal polynomials.