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

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2008
• Main Author: De Bie, H.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2008
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/147996
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: An Alternative Definition of the Hermite Polynomials Related to the Dunkl Laplacian / H. De Bie // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 24 назв. — англ.

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 generali...