2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/113875We analyze the polynomials $H_{n}^{r}(x)$ considered by Gould and Hopper, which generalize the classical Hermite polynomials. We present the main properties of $H_{n}^{r}(x)$ and derive asymptotic approximations for large values of $n$ from their differential-difference equation, using a discrete ray method. We give numerical examples showing the accuracy of our formulas.28 pages, 6 figuresClassical Analysis and ODEs33C45 (Primary) 34E05, 34E20 (Secondary)text