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| Global Asymptotics of Krawtchouk Polynomials — a Riemann-Hilbert Approach |
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Citation： |
Dan DAI,Roderick WONG.Global Asymptotics of Krawtchouk Polynomials — a Riemann-Hilbert Approach[J].Chinese Annals of Mathematics B,2007,28(1):1~34 |
| Page view： 1323
Net amount： 940 |
Authors： |
Dan DAI; Roderick WONG |
Foundation： |
Project supported by the the Research Grants Council of the Hong Kong Special Administrative Region, China (No. CityU 102504). |
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| 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 $\frac n N$ tends to a limit $c \in (0,1)$ as $n
\rightarrow \infty$. 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. |
Keywords： |
Global asymptotics, Krawtchouk polynomials, Parabolic cylinder functions, Airy functions, Riemann-Hilbert problems |
Classification： |
41A60, 33C45 |
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