# Cauchy's residue sore thumb

## TL;DR

This paper revisits Cauchy's original complex analysis method for real integrals, highlighting its simplicity and historical significance despite initial lack of rigorous foundations.

## Contribution

It reformulates Cauchy's residue method in a rigorous way, demonstrating its elegance compared to modern residue calculus.

## Key findings

- Cauchy's original approach is simpler than modern methods
- Proper formulation restores rigor to Cauchy's method
- Historical perspective on complex integral computation

## Abstract

Cauchy's method from two centuries ago for computing integrals along the real axis by passing into the complex plane is not rigorous by present-day standards. Yet when properly formulated, his original approach is simpler than modern presentations of the residue calculus.