Global Asymptotics of Krawtchouk Polynomials——a Riemann-Hilbert Approach

在这篇论文，我们学习 Krawtchouk polynomialsK_n^N 的 asymptotics (z； p， q ) 作为度， n 变得大。当参数 n/N 的比率作为 n →∞趋于到限制 c ∈(0,1 ) 时， Asymptotic 扩大被获得。结果在取决于 c 和 p 的价值的复杂 z 飞机在一个或二个区域是全球性有效的；特别地，他们在包含这些多项式是直角的上间隔的区域是有效的。我们的方法是 Riemann-Hilbert 途径由 Deift 和周介绍了的基于的在。

In this paper, we study the asymptotics of the Krawtchouk polynomials Kn^N（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 E （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 Delft and Zhou.