| We present a mathematica package that performs the symbolic calculation of integrals of the form
\\begin{equation}
\\int^{\\infty}_0 e^{-x/u} x^n j_{\\nu} (x) j_{\\mu} (x) dx \\,
\\end{equation}
where $j_{\\nu} (x)$ and $j_{\\mu} (x)$ denote spherical Bessel functions of integer orders, with $\\nu \\ge 0$ and $\\mu \\ge 0$.
With the real parameter $u>0$ and the integer $n$, convergence of the integral requires that $n+\\nu +\\mu \\ge 0$. The package provides analytical result for the integral in its most simplified form. The novel symbolic method employed enables
the calculation of a large number of integrals of the above form in a fraction of the time required for conventional numerical and Mathematica based brute-force methods. We test the accuracy of such analytical expressions by comparing the results with their numerical counterparts. |
