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

Abstract

Li-Chien Shen developed a family of elliptic functions from the hypergeometric function ${}_2{F}_1(\frac{1}{3},\frac{2}{3};\frac{1}{2};\bullet )$. We comment on this development, offering some new proofs.