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Laplace transform of spherical Bessel functions

A. Ludu·R. F. O'Connell
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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.

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A. Ludu, R. F. O'Connell. 2002-01-18. Laplace transform of spherical Bessel functions. https://doi.org/10.1238/physica.regular.065a00369

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