Global Asymptotics of Krawtchouk Polynomials – a Riemann-Hilbert Approach*

Abstract

In this paper, we study the asymptotics of the Krawtchouk polynomials K N n (z; p, q) as the degree n becomes large. Asymptotic expansions are obtained when the ratio of the parameters n/N tends to a limit c ∈ (0, 1) as n → ∞. The results are globally valid in one or two regions in the complex z-plane depending on the values of c and p; in particular, they are valid in regions containing the interval on which these polynomials are orthogonal. Our method is based on the Riemann-Hilbert approach introduced by Deift and Zhou.2000 Mathematics Subject Classification. Primary 41A60, 33C45.

Uniform Asymptotic Expansions for the Discrete Chebyshev Polynomials

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