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Please use this identifier to cite or link to this item: http://hdl.handle.net/2031/4621

Title: Global asymptotics of Hermite polynomials via Riemann-Hilbert approach
Other Titles: Ji yu Riemann-Hilbert fang fa de Hermite duo xiang shi quan ju jian jin zhan kai
基於 Riemann-Hilbert 方法的 Hermite 多項式全局漸進展開
Authors: Zhang, Lun (張侖)
Department: Dept. of Mathematics
Degree: Master of Philosophy
Issue Date: 2006
Publisher: City University of Hong Kong
Subjects: Hermite polynomials
Riemann-Hilbert problems
Notes: CityU Call Number: QA404.5.Z45 2006
Includes bibliographical references (leaves 43-44)
Thesis (M.Phil.)--City University of Hong Kong, 2006
i, 44 leaves : ill. ; 30 cm.
Type: Thesis
Abstract: In this thesis, we study the asymptotic behavior of the Hermite polynomials Hn((2n+ 1)1/2z) as n → ∞. A globally uniform asymptotic expansion is obtained for z in an unbounded region containing the right half-plane Re z ≥ 0. A corresponding expan- sion can also be given for z in the left half-plane by using the symmetry property of the Hermite polynomials. Our approach is based on the steepest-descent method for Riemann-Hilbert problems introduced by Deift and Zhou. At the end of the thesis, we compare our result with that of Olver obtained by using differential equation theory.
Online Catalog Link: http://lib.cityu.edu.hk/record=b2147192
Appears in Collections:MA - Master of Philosophy

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