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

## TL;DR

This paper discusses the development of elliptic functions derived from a specific hypergeometric function, providing new proofs and insights into Li-Chien Shen's work.

## Contribution

It offers new proofs and commentary on the construction of elliptic functions from the hypergeometric function $_2F_1(1/3, 2/3; 1/2; ullet)$ by Li-Chien Shen.

## Key findings

- New proofs of elliptic functions from hypergeometric functions
- Enhanced understanding of Shen's elliptic function family
- Clarification of the mathematical structure involved

## Abstract

Li-Chien Shen developed a family of elliptic functions from the hypergeometric function $_2F_1(\frac{1}{3}, \frac{2}{3} ; \frac{1}{2} ; \bullet)$. We comment on this development, offering some new proofs.