A deformation of Hermite polynomials

Abstract

We propose and study the properties of a set of polynomials $M_{n\alpha ,H}^s(z)$, $C_{n\alpha ,H}^s(z)$ $W_{n\alpha ,H}^s(z)$ with $n,s\in N$ $;\alpha =\pm 1;$and where $H$ stands for Hermite ; the ''root '' polynomial >.These polynomials are obtained from a deformation of Hermite polynomials $H_n(z).$The structure underlying the deformation seems quite general and not only restricted to Hermite polynomials.

16 pages, Latex