February 13th, 2018

лошадь, диаграмма, Фейнман

О связи между сферическими и тороидальными гармониками

Relationships between solid spherical and toroidal harmonics: https://arxiv.org/abs/1802.03484

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.

Comments: 9 pages, 1 figure, 2 Matlab files attached as supplementary