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.
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页码：101 / 123
页数：23
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