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q-Dunkl-classical q-Hermite type polynomials

Abstract. In this paper, we introduce two symmetric q-Dunkl-classical orthogonal polynomial sets generalizing the Hermite polynomials as range of discrete q-Hermite polynomials I and II by a suitable orthogonality preserving operator. Then, we state some of their properties: explicit expressions, recurrence relations, generating functions, inversion formulas, linear functionals and components. We conclude by locating these polynomials among orthogonal polynomials generalizing Hermite polynomials and classified according to lowering operators.