%0 Journal Article
%T Asymptotic Properties of Krawtchouk Polynomials<br>Krawtchouk多项式的渐近性态
%A ZHU Xiaofeng
%A ZHANG Meirong
%A LI Xiuchun
%A <br>朱晓峰
%A 张梅荣
%A 李秀淳
%J 系统科学与数学
%D 2008
%I 
%X In this paper, the asymptotic properties of Krawtchouk polynomials and their zeros are investigated. Firstly, a uniform asymptotic expansion for Krawtchouk polynomials $K_n \left( {\lambda N}\right)$ ($\lambda = \frac{x}{N},0 < \lambda < 1)$ is derived, for any fixed $v = \frac{n}{N} \in (0,q)$ or $(0,p)$. Then asymptotic expansions of their zeros are given. Finally the error bound $O(n^{-\frac{4}{3}})$ is obtained.
%K Krawtchouk polynomial
%K zero
%K error
%K asymptotic properties<br>Krawtchouk多项式
%K 零点
%K 误差
%K 渐近性态.
%K 多项式
%K 渐近性态
%K POLYNOMIALS
%K PROPERTIES
%K 分析
%K 误差限
%K 一致有效渐近展开式
%K 固定
%K 研究
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=6E709DC38FA1D09A4B578DD0906875B5B44D4D294832BB8E&cid=37F46C35E03B4B86&jid=0CD45CC5E994895A7F41A783D4235EC2&aid=46A6BA204C639C63502EAD2F569D3EAD&yid=67289AFF6305E306&vid=D3E34374A0D77D7F&iid=E158A972A605785F&sid=42D7028D961473F8&eid=D8AE57480552698F&journal_id=1000-0577&journal_name=系统科学与数学&referenced_num=0&reference_num=6