A Recipe For Obtaining Algebraic Addition Theorems Of The Weierstrass Elliptic Function
Complex Variables
2025-11-20 v2 Classical Analysis and ODEs
Abstract
In this paper, we present a general method for obtaining addition theorems of the Weierstrass elliptic function 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.
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Cite
@article{arxiv.2504.12366,
title = {A Recipe For Obtaining Algebraic Addition Theorems Of The Weierstrass Elliptic Function},
author = {Efe Gürel},
journal= {arXiv preprint arXiv:2504.12366},
year = {2025}
}
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9 pages