Laplace transform of spherical Bessel functions
Mathematical Physics
2009-11-07 v2 Algebraic Geometry
math.MP
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.
Cite
@article{arxiv.math-ph/0102020,
title = {Laplace transform of spherical Bessel functions},
author = {A. Ludu and R. F. O'Connell},
journal= {arXiv preprint arXiv:math-ph/0102020},
year = {2009}
}
Comments
5 pages LATEX, no figures. Accepted 2002, Physica Scripta