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

Diego Dominici

Published 2006-01-04Version 1

We 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.