Asymptotic analysis of the Hermite polynomials from their differential-difference equation

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/107392We analyze the Hermite polynomials $H_{n}(x)$ and their zeros asymptotically, as $n\to\infty.$ We obtain asymptotic approximations from the differential-difference equation which they satisfy, using the ray method. We give numerical examples showing the accuracy of our formulas.21 pages, 2 figuresClassical Analysis and ODEs33C45 (Primary) 34E05, 34E20 (Secondary)Asymptotic analysis of the Hermite polynomials from their differential-difference equationtext