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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.
Keywords: Orthogonal polynomials; symmetric orthogonal polynomials; q-Dunkl operator; generalized Hermite polynomials; discrete q-Hermite polynomials I and II
The authors would like to thank the referee for his/her remarks.
Received: 2012-12-24
Accepted: 2013-5-14
Published Online: 2014-5-13
Published in Print: 2014-6-1
© 2014 by Walter de Gruyter Berlin/Boston
