A comparison of scalar multipole expansions
- 1 December 1984
- journal article
- Published by AIP Publishing in Journal of Applied Physics
- Vol. 56 (11) , 3039-3049
- https://doi.org/10.1063/1.333885
Abstract
Scalar multipole expansions have been widely used in many areas of physics as general solutions to Laplace’s equation. However, comparison of work by different authors is often complicated by the existence of several different forms of multipole expansions in different coordinate systems. In this paper we compare the spherical harmonic, Taylor’s series, direction cosine and traceless tensor expansions and present models of dipole configurations that in the proper limit give the individual multipoles. These pictures simplify the comparison of the series and aid in interpretation of the various multipole moments.This publication has 3 references indexed in Scilit:
- Two Theorems Concerning the Quadrupole Applicable to ElectrocardiographyIEEE Transactions on Biomedical Engineering, 1965
- On multipole representation of current generatorsBulletin of Mathematical Biology, 1962
- Cartesian Tensor Scalar Product and Spherical Harmonic Expansions in Boltzmann's EquationPhysical Review B, 1960