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As contributions to the Ramanujan theory of elliptic functions to alternativebases, Li-Chien Shen has developed families of elliptic functions from thehypergeometric functions $F(\tfrac{1}{3}, \tfrac{2}{3}; \tfrac{1}{2} ;\bullet)$ and $F(\tfrac{1}{4}, \tfrac{3}{4}; \tfrac{1}{2} ; \bullet)$. We applyhis methods to the hypergeometric function $F(\tfrac{1}{6}, \tfrac{5}{6};\tfrac{1}{2} ; \bullet)$.

Nonelliptic functions from $F(\frac{1}{6}, \frac{5}{6} ; \frac{1}{2} ; \bullet)$