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Elliptic Functions
With careful standardization of argument conventions, Mathematica provides full coverage of all standard types of elliptic functions, with arbitrary-precision numerical evaluation for complex values of all parameters, as well as extensive symbolic transformations and simplifications.
Jacobi Elliptic Functions
JacobiSN  ▪ JacobiCN  ▪ JacobiDN  ▪ JacobiCD  ▪ JacobiCS  ▪ JacobiDC  ▪ JacobiDS  ▪ JacobiNC  ▪ JacobiND  ▪ JacobiNS  ▪ JacobiSC  ▪ JacobiSD
Inverse Jacobi Elliptic Functions
Weierstrass Elliptic Functions
Inverse Weierstrass Elliptic Functions
Theta Functions
Elliptic Exponential Functions
    
JacobiAmplitude convert from argument u and parameter m to amplitude Phi
EllipticNomeQ convert from parameter m to nome q
InverseEllipticNomeQ convert from nome q to parameter m
    
WeierstrassInvariants convert from half-periods to invariants
WeierstrassHalfPeriods convert from invariants to half-periods
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