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

Abstract

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