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

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

2006-01-04

arxiv.org/abs/math/0601078v1

Mathematics

Classical Analysis and ODEs

21 pages, 2 figures

Scientific paper

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.

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