Elliptic Functions

With careful standardization of argument conventions, the Wolfram Language 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.

ReferenceReference

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

InverseWeierstrassP

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