# Electrostatic equilibria on the unit circle via Jacobi polynomials

@article{Johnson2020ElectrostaticEO,
title={Electrostatic equilibria on the unit circle via Jacobi polynomials},
author={Krista E Johnson and Brian Simanek},
journal={arXiv: Mathematical Physics},
year={2020}
}
• Published 20 August 2020
• Mathematics
• arXiv: Mathematical Physics
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.
2 Citations

## Figures from this paper

HIGH-LOW TEMPERATURE DUALITIES FOR THE CLASSICAL β-ENSEMBLES
The loop equations for the [Formula: see text]-ensembles are conventionally solved in terms of a [Formula: see text] expansion. We observe that it is also possible to fix [Formula: see text] and
High-low temperature dualities for the classical $\beta$-ensembles
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