Laplace transform of spherical Bessel functions
arXiv:math-ph/0102020 · doi:10.1238/Physica.Regular.065a00369
Abstract
We provide a simple analytic formula in terms of elementary functions for the Laplace transform j_{l}(p) of the spherical Bessel function than that appearing in the literature, and we show that any such integral transform is a polynomial of order l in the variable p with constant coefficients for the first l-1 powers, and with an inverse tangent function of argument 1/p as the coefficient of the power l. We apply this formula for the Laplace transform of the memory function related to the Langevin equation in a one-dimensional Debye model.
arXiv comment5 pages LATEX, no figures. Accepted 2002, Physica Scripta