Capacity of several aligned segments

TL;DR

This paper derives a universal theta function formula for calculating the logarithmic capacity of multiple aligned segments on a line, extending previous work on fewer segments.

Contribution

It introduces a new universal formula for the capacity of several segments, generalizing earlier results for two and three segments.

Findings

Derived a theta function-based formula for multiple segments' capacity

Extended known results from two and three segments to several segments

Provides a unified approach for calculating capacities of aligned segments

Abstract

In this note we present a universal formula in terms of theta functions for the Log- capacity of several segments on a line. The case of two segments was studied by N.I.Akhiezer (1930); three segments were considered by A.Sebbar and T.Falliero (2001).