Argument-recursive computation of Legendre polynomials and its application to the time domain near-to-far-field spherical-multipole analysis

An efficient x-recursive numerical scheme is presented to compute Legendre polynomials P
n
(x) and their derivatives P'
n
(x) on the interval (0, 1) for a fixed-order
$n\in\mathbb{N}$
. The numerical properties are discussed and, as an example of use in computational electromagnetics, the method is applied to improve a recently proposed spherical-multipole based time domain near-to-far-field transformation algorithm.