# Elliptic functions from $F(\frac{1}{4}, \frac{3}{4} ; \frac{1}{2} ; \bullet)$

## TL;DR

This paper explores elliptic functions derived from a specific hypergeometric function, providing new proofs that avoid theta functions, thus offering a novel perspective on their mathematical structure.

## Contribution

It introduces alternative proofs for elliptic functions from a hypergeometric function, bypassing the traditional reliance on theta functions.

## Key findings

- New proofs of elliptic functions without theta functions
- Enhanced understanding of hypergeometric-based elliptic functions
- Potential simplifications in elliptic function theory

## Abstract

We reconsider the elliptic functions that are generated from the hypergeometric function $F(\tfrac{1}{4}, \tfrac{3}{4}; \tfrac{1}{2} ; \bullet)$ by Li-Chien Shen, presenting fresh proofs that do not require the use of theta functions.