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An Alternative Definition of the Hermite Polynomials Related to the Dunkl Laplacian
Symmetry, integrability and geometry: methods and applications, Tome 4 (2008) Cet article a éte moissonné depuis la source Math-Net.Ru

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We introduce the so-called Clifford–Hermite polynomials in the framework of Dunkl operators, based on the theory of Clifford analysis. Several properties of these polynomials are obtained, such as a Rodrigues formula, a differential equation and an explicit relation connecting them with the generalized Laguerre polynomials. A link is established with the generalized Hermite polynomials related to the Dunkl operators (see [Rösler M., Comm. Math. Phys. 192 (1998), 519–542, q-alg/9703006]) as well as with the basis of the weighted $L^2$ space introduced by Dunkl.
Keywords: Hermite polynomials; Dunkl operators; Clifford analysis. 
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     author = {Hendrik De Bie},
     title = {An {Alternative} {Definition} of the {Hermite} {Polynomials} {Related} to the {Dunkl} {Laplacian}},
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Hendrik De Bie. An Alternative Definition of the Hermite Polynomials Related to the Dunkl Laplacian. Symmetry, integrability and geometry: methods and applications, Tome 4 (2008). http://geodesic.mathdoc.fr/item/SIGMA_2008_4_a92/

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