The Mehler Formula for the Generalized Clifford.Hermite Polynomials

Authors
Brackx, F. de Schepper, N. Kou, K. I. Sommen, F.
Citation
F. Brackx, et al., The Mehler Formula for the Generalized Clifford.Hermite Polynomials, Acta mathematica Sinica. English series (Print) , 23(4), 2007, pp. 697-704
Journal title
Acta mathematica Sinica. English series (Print) → ACNP
ISSN journal
14398516
Volume
23
Issue
4
Year of publication
2007
Pages
697 - 704
Database
ACNP
SICI code
Abstract
The Mehler formula for the Hermite polynomials allows for an integral representation of the one.dimensional Fractional Fourier transform. In this paper, we introduce a multi.dimensional Fractional Fourier transform in the framework of Clifford analysis. By showing that it coincides with the classical tensorial approach we are able to prove Mehler.s formula for the generalized Clifford.Hermite polynomials of Clifford analysis.