Relationships between solid spherical and toroidal harmonics
Mathematical Physics
2019-12-23 v3 math.MP
Classical Physics
Abstract
We derive new relationships expressing solid spherical harmonics as series of toroidal harmonics and vice versa. The expansions include regular and irregular spherical harmonics, ring and axial toroidal harmonics of even and odd parity about the plane of the torus. The expansion coefficients are given in terms of a recurrence relation. As an example application we apply one of the expansions to express the potential of a charged conducting torus on a basis of spherical harmonics.
Cite
@article{arxiv.1802.03484,
title = {Relationships between solid spherical and toroidal harmonics},
author = {Matt Majic and Eric C. Le Ru},
journal= {arXiv preprint arXiv:1802.03484},
year = {2019}
}
Comments
Main results are also published in JQSRT "Electrostatic T-matrix for a torus on bases of toroidal and spherical harmonics" Matt Majic. 13 pages, 6 figure, 6 Matlab codes attached as ancillary files