A Recipe For Obtaining Algebraic Addition Theorems Of The Weierstrass Elliptic Function

Abstract

In this paper, we present a general method for obtaining addition theorems of the Weierstrass elliptic function $\wp (z)$ in terms of given parameters. We obtain the classical addition theorem for the Weierstrass elliptic function as a special case. Furthermore, we give novel two-term addition, three-term addition, duplication and triplication formulas. New identities for elliptic invariants are also proven.

9 pages