Asymptotic analysis of the Krawtchouk polynomials by the WKB method
Classical Analysis and ODEs
2007-05-23 v2
Abstract
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.
Cite
@article{arxiv.math/0501042,
title = {Asymptotic analysis of the Krawtchouk polynomials by the WKB method},
author = {Diego Dominici},
journal= {arXiv preprint arXiv:math/0501042},
year = {2007}
}
Comments
41 pages, 14 figures