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

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arxiv math/0601078 v1 pith:H76N6ARI submitted 2006-01-04 math.CA

Diego Dominici This is my paper · ORCID
classification math.CA
keywords asymptoticdifferential-differenceequationhermitepolynomialsaccuracyanalysisanalyze
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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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