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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.
Reference
Jacobi Elliptic Functions
JacobiSN ▪ JacobiCN ▪ JacobiDN ▪ JacobiCD ▪ JacobiCS ▪ JacobiDC ▪ JacobiDS ▪ JacobiNC ▪ JacobiND ▪ JacobiNS ▪ JacobiSC ▪ JacobiSD
Inverse Jacobi Elliptic Functions
InverseJacobiSN ▪ InverseJacobiCN ▪ InverseJacobiDN ▪ InverseJacobiCD ▪ InverseJacobiCS ▪ InverseJacobiDC ▪ InverseJacobiDS ▪ InverseJacobiNC ▪ InverseJacobiND ▪ InverseJacobiNS ▪ InverseJacobiSC ▪ InverseJacobiSD
Weierstrass Elliptic Functions
WeierstrassP ▪ WeierstrassPPrime ▪ WeierstrassSigma ▪ WeierstrassZeta
Inverse Weierstrass Elliptic Functions
Theta Functions
EllipticTheta ▪ EllipticThetaPrime ▪ SiegelTheta
NevilleThetaC ▪ NevilleThetaD ▪ NevilleThetaN ▪ NevilleThetaS
Elliptic Exponential Functions
EllipticExp ▪ EllipticExpPrime ▪ EllipticLog
JacobiAmplitude — convert from argument 
and parameter 
to amplitude 
EllipticNomeQ — convert from parameter 
to nome 
InverseEllipticNomeQ — convert from nome 
to parameter 
WeierstrassInvariants — convert from half-periods to invariants
WeierstrassHalfPeriods — convert from invariants to half-periods
