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

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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

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Classical Analysis and ODEs, 33C45 (Primary) 34E05, 34E20 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/107392

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0601078
 http://arxiv.org/abs/math/0601078

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arXiv