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Laplace Transform of Spherical Bessel Functions

A Ludu1 and R F O'Connell2

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We provide a simple analytic formula in terms of elementary functions for the Laplace transform tilde jl(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.


PACS

02.30.Uu Integral transforms

02.30.Gp Special functions

MSC

44A10 Laplace transform

33C10 Bessel and Airy functions, cylinder functions, 0F1

Subjects

Mathematical physics

Dates

Issue 5 (2002)

Received 14 May 2001



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