On a theorem concerning the elliptic functions

TL;DR

This paper presents a translation of Phragmen's proof of Weierstrass' theorem, which characterizes all analytic functions with an algebraic addition theorem, providing historical and mathematical insight.

Contribution

It offers the first published translation of Phragmen's proof, clarifying the original argument and its significance in the theory of elliptic functions.

Findings

Clarifies the proof of Weierstrass' theorem

Highlights the historical development of elliptic functions

Provides insights into algebraic addition theorems

Abstract

This is a literal word-for-word translation from the French of Phragmen's proof (the first such published) of Weierstrass' famous theorem characterizing all analytic functions which possess an algebraic addition theorem.