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Asymptotic analysis of the Askey-scheme. I: From Krawtchouk to Charlier. (English) Zbl 1124.33008

Author’s summary: The author analyze the Charlier polynomials \(C_{n}(x)\) and their zeros asymptotically as \(n \rightarrow \infty\). He obtains asymptotic approximations, using the limit relation between the Krawtchouk and Charlier polynomials, involving some special functions. We give numerical examples showing the accuracy of our formulas.

MSC:

33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
34E05 Asymptotic expansions of solutions to ordinary differential equations
33C10 Bessel and Airy functions, cylinder functions, \({}_0F_1\)
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