Hyperasymptotic expansions of the modified Bessel function of the third kind of purely imaginary order

被引：2

作者：

Shi, Wei ^{[1
]}

Wong, R. ^{[2
]}

机构：

[1] Wuhan Univ, Dept Math, Wuhan 430072, Hubei, Peoples R China

[2] City Univ Hong Kong, Dept Math, Kowloon, Hong Kong, Peoples R China

来源：

ASYMPTOTIC ANALYSIS | 2009年 / 63卷 / 1-2期

关键词：

modified Bessel function of the third kind of purely imaginary order; hyperasymptotic expansion; Hadamard series; LAPLACE-TYPE INTEGRALS; LINEAR-DIFFERENTIAL EQUATIONS; HADAMARD EXPANSIONS; ASYMPTOTIC EXPANSIONS; THIRD KIND; VARIABLES; ARGUMENT;

D O I：

10.3233/ASY-2008-0930

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we use a new method to derive hyperasymptotic expansions for the modified Bessel function of the third kind of purely imaginary order. Our approach is based on the method of Hadamard-series expansion developed by Paris (Proc. Roy. Soc. Lond. A 457 (2001), 2855-2869). Modifications are made to deal with the presence of an infinite number of saddle points, and numerical computation is used to illustrate the accuracy of our results.

引用

页码：101 / 123

页数：23

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