Integrating products of Bessel functions with an additional exponential or rational factor

Abstract We provide two Matlab programs to compute integrals of the formunderover(∫, 0, ∞) e ^(- c x)x ^munderover(∏, i = 1, k) J _(νi)(a _ix) d x and underover(∫, 0, ∞) frac(x ^m , r ^2+ x ^2 ) underover(∏, i = 1, k) J _(νi)(a _ix) d x with J _(νi)... Title of program: BESSELINTR, BESSELINTC Catalogue Id: AEAH_v1_0 Nature of problem The problem consists in integrating an arbitrary product of Bessel functions with an additional rational or exponential factor over a semi-infinite interval. Difficulties arise from the irregular oscillatory behaviour and the possible slow decay of the integrand, which prevents truncation at a finite point. Versions of this program held in the CPC repository in Mendeley Data AEAH_v1_0; BESSELINTR, BESSELINTC; 10.1016/j.cpc.2007.11.010 This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2019)摘要 我们提供两款Matlab程序，用于计算如下两类积分形式： $$int_{0}^{infty} e^{-cx}x^m prod_{i=1}^{k} J_{ u_i}(a_i x) mathrm{d}x$$ 以及 $$int_{0}^{infty} frac{x^m}{r^2 + x^2} prod_{i=1}^{k} J_{ u_i}(a_i x) mathrm{d}x$$ 其中$J_{ u_i}$为$ u_i$阶贝塞尔函数（Bessel function）…… 程序名称：BESSELINTR、BESSELINTC 目录编号：AEAH_v1_0 问题描述 本问题需在半无限区间上，对包含任意个贝塞尔函数乘积并附带有理因子或指数因子的被积函数进行积分。由于被积函数存在不规则振荡行为与潜在的缓慢衰减特性，导致无法在有限点处截断积分区间，由此造成了计算难题。 本程序收录于Mendeley数据平台的CPC程序库中，相关信息如下： 版本：AEAH_v1_0；关联程序名称：BESSELINTR、BESSELINTC；DOI：10.1016/j.cpc.2007.11.010 本程序源自贝尔法斯特女王大学（1969-2019年）维护的CPC程序库。