Asymptotic Properties of Krawtchouk Polynomials
Krawtchouk多项式的渐近性态

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.