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 ℘(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.
Fields of Study & Subjects
Advanced Mathematical Identities
Mathematical functions and polynomials
Algebraic Geometry and Number Theory
Publication details
- Journal / source
- Integral Transforms and Special Functions
- Pages
- 1–12
- Publication date
- 9 February 2026
- Language
- EN