2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/56639We propose and study the properties of a set of polynomials $M_{nα, H\ }^{s}(z)$, $C_{nα, H}^{s}(z)$ $W_{nα, H}^{s}(z)$ with $n,s\in N$ $;α=\pm 1;$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, LatexMathematical PhysicsClassical Analysis and ODEsFunctional Analysis33C45;34A35text