We provide a simple analytic formula in terms of elementary functions for the Laplace transform j̃l(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.
Publication Source (Journal or Book title)
Ludu, A., & O'Connell, R. (2002). Laplace transform of spherical Bessel functions. Physica Scripta, 65 (5), 369-372. https://doi.org/10.1238/Physica.Regular.065a00369