A Note on the Dunkl-Appell Orthogonal Polynomials

Authors : Mabrouk Sghaier

Pages : 263-267

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Publication Date : 2020-10-27

Article Type : Research

Abstract :This paper deals with the problem of finding all orthogonal polynomial sets which are also $T_{\mu}$-Appell where $T_{\mu}, \mu \in \mathbb{C}$ is the Dunkl operator. The resulting polynomials reduce to Generalized Hermite polynomials $\{{{H}}_n(\mu)\}_{n\geq0}$.                                                                                                                                                                                                                                                                                                            
Keywords : Orthogonal polynomials, Dual sequence, Dunkl operator