Résumé du preprint Irfu-09-192

Irfu-09-192
Symbolic integration of a product of two spherical bessel functions with an additional exponential and polynomial factor
B. Gebremariam, T. Duguet, S. K. Bogner
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.