Resurgence relation and global asymptotic analysis of orthogonal polynomials via the Riemann-Hilbert approach

被引：1

作者：

Xu ShuaiXia ^{[1
]}

Zhao YuQiu ^{[1
]}

机构：

[1] Sun Yat Sen Univ, Zhongshan Univ, Dept Math, Guangzhou 510275, Guangdong, Peoples R China

来源：

SCIENCE CHINA-MATHEMATICS | 2011年 / 54卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Riemann-Hilbert approach; resurgence relation; uniform asymptotics; orthogonal polynomials; Hermite polynomials; Airy function; UNIFORM ASYMPTOTICS; EXPANSIONS;

D O I：

10.1007/s11425-010-4151-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A global asymptotic analysis of orthogonal polynomials via the Riemann-Hilbert approach is presented, with respect to the polynomial degree. The domains of uniformity are described in certain phase variables. A resurgence relation within the sequence of Riemann-Hilbert problems is observed in the procedure of derivation. Global asymptotic approximations are obtained in terms of the Airy function. The system of Hermite polynomials is used as an illustration.

引用

页码：661 / 679

页数：19

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