Abstract
Based on properties of the hypergeometric series 2 F 1 ( 1 3 , 2 3 ; 1 2 ; z ) {}_{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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