Global asymptotics of krawtchouk polynomials - A riemann-hilbert approach

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Original languageEnglish
Pages (from-to)1-34
Journal / PublicationChinese Annals of Mathematics. Series B
Issue number1
Publication statusPublished - Jan 2007


In this paper, we study the asymptotics of the Krawtchouk polynomials KnN (z;p,q) as the degree n becomes large. Asymptotic expansions are obtained when the ratio of the parameters n/N tends to a limit c (0, 1) as n → ∞. The results are globally valid in one or two regions in the complex z-plane depending on the values of c and p; in particular, they are valid in regions containing the interval on which these polynomials are orthogonal. Our method is based on the Riemann-Hilbert approach introduced by Deift and Zhou. © Springer-Verlag Berlin Heidelberg 2007.

Research Area(s)

  • Airy functions, Global asymptotics, Krawtchouk polynomials, Parabolic cylinder functions, Riemann-Hilbert problems