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Computational Methods and Function Theory

, Volume 4, Issue 1, pp 189–226 | Cite as

Asymptotic Expansion of the Krawtchouk Polynomials and their Zeros

  • Wei-Yuan Qiu
  • Roderick Wong
Article

Abstract

Let \(K_{n}^{N}(x;p,q)\) be the Krawtchouk polynomials and μ = N/n. An asymptotic expansion is derived for \(K_{n}^{N}(x;p,q)\), when x is a fixed number. This expansion holds uniformly for μ in [1,∞), and is given in terms of the confluent hypergeometric functions. Asymptotic approximations are also obtained for the zeros of \(K_{n}^{N}(x;p,q)\) in various cases depending on the values of p, q and μ.

Keywords

Krawtchouk polynomials asymptotic expansions confluent hypergeometric functions zeros 

2000 MSC

33C45 41A60 

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Copyright information

© Heldermann  Verlag 2004

Authors and Affiliations

  1. 1.Department of MathematicsFudan UniversityShanghaiPeople’s Republic of China
  2. 2.Department of MathematicsCity University of Hong KongKowloonHong Kong

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