Asymptotic analysis of the Krawtchouk polynomials by the WKB method

Details Asymptotic analysis of the Krawtchouk polynomials by the WKB method Asymptotic analysis of the Krawtchouk polynomials by the WKB method

2005-01-04

arxiv.org/abs/math/0501042v2

Mathematics

Classical Analysis and ODEs

41 pages, 14 figures

Scientific paper

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.

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