## Abstract

The discovery of elliptic functions emerged from investigations of integral addition theorems. An addition theorem for a function f is a formula expressing f(u+v) in terms of f(u) and f(v). For a function defined as a definite integral with a variable upper limit, an addition theorem takes the form of an equation between the sum of two such integrals, with upper limits u and v, and an integral whose upper limit is a certain function of u and v.In this paper, we briefly sketch the role which the investigation of such addition theorems has played in the development of the theory of elliptic intgrals and elliptic functions.

## Faculty Sponsor

Aihua Li

## Recommended Citation

Barrios, Jose
(2009)
"A Brief History of Elliptic Integral Addition Theorems,"
*Rose-Hulman Undergraduate Mathematics Journal*: Vol. 10:
Iss.
2, Article 2.

Available at:
https://scholar.rose-hulman.edu/rhumj/vol10/iss2/2