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 (Formula presented.) -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 (Formula presented.) -analogue of generalized Hermite and the (Formula presented.) -analogue of generalized Gegenbauer polynomials.