| Global Asymptotics of Krawtchouk Polynomials — a Riemann-Hilbert Approach |
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| 引用本文： | Dan DAI,Roderick WONG. Global Asymptotics of Krawtchouk Polynomials — a Riemann-Hilbert Approach[J]. 数学年刊B辑(英文版), 2007, 28(1): 1-34 |
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| 作者姓名： | Dan DAI Roderick WONG |
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| 摘 要： |
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| 收稿时间： | 2012-05-06 |
Global Asymptotics of Krawtchouk Polynomials——a Riemann-Hilbert Approach |
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| Dan DAI and Roderick WONG. Global Asymptotics of Krawtchouk Polynomials——a Riemann-Hilbert Approach[J]. Chinese Annals of Mathematics,Series B, 2007, 28(1): 1-34 |
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| Authors: | Dan DAI and Roderick WONG |
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| Affiliation: | Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong, China.;Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong, China. |
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| Abstract: | In this paper, we study the asymptotics of the Krawtchouk polynomials KnN(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. |
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| Keywords: | Global asymptotics Krawtchouk polynomials Parabolic cylinder functions Airy functions Riemann-Hilbert problems |
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