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

B. Gebremarian
T. Duguet
S.K. Bogner
Journal / Anthology

Computer Physics Communications
Year: 2010
Volume: 181
Issue: 6
Page range: 1136-1143

We present a Mathematica package that performs the symbolic calculation of integrals of the form ∞  0 e−x/uxn jν (x) jμ(x)dx (1) where jν (x) and jμ(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 implementations succeed in evaluating these integrals, the novel symbolic method implemented in this work obtains the same result and in general, it takes a fraction of the time required for the direct implementation. We test the accuracy of such analytical expressions by comparing the results with their numerical counterparts.