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Symmetry, Integrability and Geometry: Methods and Applications, 2008, Volume 4, 093, 11 pp.
DOI: https://doi.org/10.3842/SIGMA.2008.093 (Mi sigma346) 		 
This article is cited in 3 scientific papers (total in 3 papers)

An Alternative Definition of the Hermite Polynomials Related to the Dunkl Laplacian

Hendrik De Bie

Department of Mathematical Analysis, Faculty of Engineering, Ghent University, Krijgslaan 281, 9000 Gent, Belgium
Full-text PDF (240 kB) Citations (3)
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DOI: https://doi.org/10.3842/SIGMA.2008.093
Abstract: 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.
Received: October 7, 2008; in final form December 18, 2008; Published online December 28, 2008
Bibliographic databases:
Document Type: Article
MSC: 33C80; 33C45; 30G35
Language: English
Citation: Hendrik De Bie, “An Alternative Definition of the Hermite Polynomials Related to the Dunkl Laplacian”, SIGMA, 4 (2008), 093, 11 pp.
Citation in format AMSBIB
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    		Symmetry, Integrability and Geometry: Methods and Applications
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