# Conformal module of the exterior of two rectilinear slits

## TL;DR

This paper derives formulas for the moduli of planar ring domains with complements as linear segments using Weierstrass elliptic functions, supported by numerical tests to validate the results.

## Contribution

It introduces explicit formulas for the moduli of specific ring domains in terms of elliptic functions, advancing the understanding of conformal invariants in geometric function theory.

## Key findings

- Formulas for moduli in terms of Weierstrass elliptic functions
- Numerical validation of the derived formulas
- Enhanced understanding of conformal invariants for domains with linear segment complements

## Abstract

We study moduli of planar ring domains whose complements are linear segments and establish formulas for their moduli in terms of the Weierstrass elliptic functions. Numerical tests are carried out to illuminate our results.