%0 Journal Article %T Asymptotic analysis of the Hermite polynomials from their differential-difference equation %A Diego Dominici %J Mathematics %D 2006 %I arXiv %X 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. %U http://arxiv.org/abs/math/0601078v1