On the theory of elliptic functions based on ₂𝐹₁(\frac{1}3,\frac{2}3;\frac{1}2;𝑧)

Shen, Li-Chien

doi:10.1090/S0002-9947-04-03600-1

On the theory of elliptic functions based on ${}_{2}F_{1}(\frac {1}{3},\frac {2}{3};\frac {1}{2};z)$
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Trans. Amer. Math. Soc. 357 (2005), 2043-2058 Request permission

Abstract:

Based on properties of the hypergeometric series ${}_{2}F_{1}(\frac {1}{3},\frac {2}{3};\frac {1}{2};z)$, we develop a theory of elliptic functions that shares many striking similarities with the classical Jacobian elliptic functions.

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