A Study of Symmetric q-Dunkl-Classical Orthogonal q-Polynomials Through a Second Structure Relation

This paper establishes a new characterization of symmetric q-Dunkl-classical orthogonal polynomials through a second structure relation. These symmetric polynomials generalize the q2-analogues of Hermite and Gegenbauer polynomials. Our main result provides a finite expansion of each polynomial in terms of its q-Dunkl derivatives, offering a new effective classification method. We derive explicit structure relations for the q2-analogue of generalized Hermite and the q2-analogue of generalized Gegenbauer polynomials.