A uniform asymptotic expansion for Krawtchouk polynomials

JOURNAL OF APPROXIMATION THEORY

卷:106

Article

Li, XC ; Wong, R

关键词: Krawtchouk polynomials;    uniform asymptotic expansion;    parabolic cylinder function;   

DOI  :  10.1006/jath.2000.3474

来源: Elsevier

【 摘 要 】

We study the asymptotic behavior of the Krawtchouk polynomial K-n((N))(x; p, q) as n --> infinity. With x = lambda N and nu = n/N, an infinite asymptotic expansion is derived, which holds uniformly for lambda and nu in compact subintervals of (0, 1). This expansion involves the parabolic cylinder function and its derivative. When nu is a fixed number, our result includes the various asymptotic approximations recently given by M. E. H. Ismail and P. Simeonov. (C) 2000 Academic Press.

【 授权许可】

Free