Ju l 2 00 7 Hermite and Gegenbauer polynomials in superspace using Clifford analysis

@inproceedings{Bie2008JuL2,
title={Ju l 2 00 7 Hermite and Gegenbauer polynomials in superspace using Clifford analysis},
author={Hendrik De Bie and Frank Sommen},
year={2008}
}

The Clifford-Hermite and the Clifford-Gegenbauer polynomials of standard Clifford analysis are generalized to the new framework of Clifford analysis in superspace in a merely symbolic way. This means that one does not a priori need an integration theory in superspace. Furthermore a lot of basic properties, such as orthogonality relations, differential equations and recursion formulae are proven. Finally, an interesting physical application of the super Clifford-Hermite polynomials is discussed… CONTINUE READING