English

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.

Keywords

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

R2 v1 2026-07-22T17:14:09.656Z