Asymptotic analysis of the Askey-scheme II: from Charlier to Hermite

Details Asymptotic analysis of the Askey-scheme II: from Charlier to Hermite Asymptotic analysis of the Askey-scheme II: from Charlier to Hermite

2005-08-15

arxiv.org/abs/math/0508264v1

Mathematics

Classical Analysis and ODEs

10 pages

Scientific paper

We analyze the Hermite polynomials $H_{n}(\xi)$ and their zeros
asymptotically as $n\to\infty,$ using the limit relation between the Charlier
and Hermite polynomials. Our formulas involve some special functions and they
yield very accurate approximations.

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