Global asymptotics of krawtchouk polynomials - A riemann-hilbert approach
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review
Author(s)
Related Research Unit(s)
Detail(s)
Original language | English |
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Pages (from-to) | 1-34 |
Journal / Publication | Chinese Annals of Mathematics. Series B |
Volume | 28 |
Issue number | 1 |
Publication status | Published - Jan 2007 |
Link(s)
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. © Springer-Verlag Berlin Heidelberg 2007.
Research Area(s)
- Airy functions, Global asymptotics, Krawtchouk polynomials, Parabolic cylinder functions, Riemann-Hilbert problems
Citation Format(s)
Global asymptotics of krawtchouk polynomials - A riemann-hilbert approach. / Dai, Dan; Wong, Roderick.
In: Chinese Annals of Mathematics. Series B, Vol. 28, No. 1, 01.2007, p. 1-34.
In: Chinese Annals of Mathematics. Series B, Vol. 28, No. 1, 01.2007, p. 1-34.
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review