Elliptic functions, infinite products and modular relations

TL;DR

This paper explores the use of infinite product expansions of the Weierstrass elliptic function and its transformations to derive new modular relations, enhancing understanding of elliptic functions and their symmetries.

Contribution

It introduces novel modular relations derived from infinite product expansions of elliptic functions and their transformations.

Findings

Derived new modular relations for elliptic functions.

Connected infinite product expansions with modular transformations.

Enhanced theoretical understanding of elliptic functions' symmetries.

Abstract

Infinite products expansions of the Weierstrass elliptic function \ $\wp(z) = \wp(z,1,\tau)$\ and $n$-order transformations allow us to provide some modular relations.