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

## Description

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)