A uniform asymptotic expansion for Krawtchouk polynomials

Abstract. Let KNn (x; p, q) be the Krawtchouk polynomials and µ = N/n. An asymptotic expansion is derived for KNn (x; p, q), when x is a fixed num-ber. 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 KNn (x; p, q) in various cases depending on the values of p, q and µ