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.
Asymptotic analysis of the Askey-scheme I: from Krawtchouk to Charlier
Asymptotic analysis of the Hermite polynomials from their differential-difference equation
Close-to-convexity of some special functions and their derivatives
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