Asymptotic analysis of the Krawtchouk polynomials by the WKB method

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We analyze the Krawtchouk polynomials K(n,x,N,p,q) asymptotically. We use singular perturbation methods to analyze them for N large with appropriate scalings of the two variables x and n. In particular, the WKB method and asymptotic matching are used. We obtain asymptotic approximations valid in the whole domain [0,N]x[0,N] involving some special functions. We give numerical examples showing the accuracy of our formulas.
41 pages, 14 figures

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

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http://salesiana.dossiersoluciones.com/handle/123456789/73760

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0501042
 http://arxiv.org/abs/math/0501042

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arXiv