Cauchy's residue sore thumb

2017/01/17 by Harold P. Boas, Boas, Harold P.
Mathematics · #30 #Complex Variables (math.CV) #FOS: Mathematics #History and Overview (math.HO) #History and Theory of Mathematics

paper · pdf · doi:10.48550/arxiv.1701.04887

openalex publication_date 2017/01/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• An integral's journey over the real line
• Real Version of Calculus of Complex Variable (I): Weierstrass Point of View
• Real Version of Calculus of Complex Variable (II): Cauchy's Point of View
• Generalizations of the Cauchy Integral Theorems
• Applications of residues and poles in solutions of some improper integrals evaluation