# Torsional Rigidity and Bergman Analytic Content of Simply Connected Regions

## TL;DR

This paper introduces a new method for calculating torsional rigidity and Bergman analytic content in simply connected regions, especially polygons, by exploiting their equality, with numerous explicit examples demonstrating its effectiveness.

## Contribution

The paper develops a novel computational approach leveraging the equality of two quantities, improving calculations for polygonal regions.

## Key findings

- Effective method for polygons
- Explicit calculations demonstrated
- Utility in complex regions

## Abstract

We exploit the equality of Bergman analytic content and torsional rigidity of a simply connected domain to develop a new method for calculating these quantities. This method is particularly suitable for the case when the region in question is a polygon. A large number of examples are computed in explicit detail to demonstrate the utility of our ideas.