Electrostatic Equilibria on the Unit Circle via Jacobi Polynomials
Mathematical Physics
2021-08-11 v1 Classical Analysis and ODEs
math.MP
Abstract
We use classical Jacobi polynomials to identify the equilibrium configurations of charged particles confined to the unit circle. Our main result unifies two theorems from a 1986 paper of Forrester and Rogers.
Keywords
Cite
@article{arxiv.2008.09176,
title = {Electrostatic Equilibria on the Unit Circle via Jacobi Polynomials},
author = {Kev Johnson and Brian Simanek},
journal= {arXiv preprint arXiv:2008.09176},
year = {2021}
}
Comments
8 pages