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

Diego Dominici
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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.

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Diego Dominici. 2006-01-04. Asymptotic analysis of the Hermite polynomials from their differential-difference equation. https://arxiv.org/abs/math/0601078

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