# Symbolic integration of a product of two spherical Bessel functions with an additional exponential and polynomial factor

## Description

Abstract We present a Mathematica package that performs the symbolic calculation of integrals of the form(1)underover(∫, 0, ∞) e^(- x / u)x^nj_ν(x) j_μ(x) d x where j_ν(x) and j_μ(x) denote spherical Bessel functions of integer orders, with ν ≥ 0 and μ ≥ 0. With the real parameter u > 0 and the integer n, convergence of the integral requires that n + ν + μ ≥ 0. The package provides analytical result for the integral in its most simplified form. In cases where direct Mathematica implementa... Title of program: SymbBesselJInteg Catalogue Id: AEFY_v1_0 Nature of problem Integration, both analytical and numerical, of products of two spherical bessel functions with an exponential and polynomial multiplying factor can be a very complex task depending on the orders of the spherical bessel functions. The Mathematica package discussed in this paper solves this problem using a novel symbolic approach. Versions of this program held in the CPC repository in Mendeley Data AEFY_v1_0; SymbBesselJInteg; 10.1016/j.cpc.2010.02.006 This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2018)