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

Abstract

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.

21 pages, 2 figures

References in corpus (1)

• The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue