Infinite integrals involving Bessel functions by contour integration
Infinite integrals involving Bessel functions by contour integration
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通过轮廓积分涉及贝塞尔函数的无限积分
DOI：
10.1080/10652469.2012.758119
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发表时间：
2013-10
期刊：
影响因子：
--
通讯作者：
林琼桂
中科院分区：
文献类型：
--
作者：
林琼桂
系统地发展了围道积分和留数定理的方法，用于计算涉及贝塞尔函数或密切相关函数的无穷积分。给出了适用于不同类型积分的三种独立的公式。
The approach of contour integration and residue theorem is systematically developed to evaluate infinite integrals involving Bessel functions or closely related ones. Three independent formulations applicable to different types of integrals are presented. The conventional formulation using Hankel functions as auxiliary functions, whose previous development leave considerable room for improvement, is fully developed. The second and third formulations, which appear unnoticed before, uses as auxiliary functions linear combinations of Bessel and Struve functions, and linear combinations of Anger and Weber functions, respectively. These functions play a crucial role as the Hankel functions do in the conventional formulation. Several general formulae are derived, each expressing an infinite integral in terms of residues. The integrands are products of rational functions, powers and Bessel (Neumann, Struve, Anger or Weber) functions, with some relation satisfied between the index of the power and the order of the Bessel or related function. Typical examples are worked out for each type of integral.
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DOI：
10.1088/0305-4470/21/23/017
发表时间：
1988-12
期刊：
Journal of Physics A
影响因子：
--
作者：
M. Lee
通讯作者：
M. Lee
DOI：
10.1088/0305-4470/24/24/010
发表时间：
1991-12
期刊：
Journal of Physics A
影响因子：
--
作者：
A. Bakulev
通讯作者：
A. Bakulev
影响因子：
2
作者：
J. E. Kilpatrick;S. Katsura;Y. Inoue
通讯作者：
J. E. Kilpatrick;S. Katsura;Y. Inoue
DOI：
10.1016/b978-0-12-817208-7.00006-6
发表时间：
2020
期刊：
General Fractional Derivatives with Applications in Viscoelasticity
影响因子：
--
作者：
Xiao-jun Yang;F. Gao;Yang Ju
通讯作者：
Xiao-jun Yang;F. Gao;Yang Ju
影响因子：
2
作者：
P. Linz;T. E. Kropp
通讯作者：
P. Linz;T. E. Kropp