2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/60824The new method for obtaining a variety of extensions of Hermite polynomials is given. As a first example a family of orthogonal polynomial systems which includes the generalized Hermite polynomials is considered. Apparently, either these polynomials satisfy the differential equation of the second order obtained in this work or there is no differential equation of a finite order for these polynomials.15 pages, no figuresQuantum AlgebraClassical Analysis and ODEs05E35 (Primary) 05E35 (Secondary)text