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
Inverse Jacobi Elliptic Functions
Weierstrass Elliptic Functions
Inverse Weierstrass Elliptic Functions
Elliptic Exponential Functions
JacobiAmplitude — convert from argument
u and parameter
m to amplitude
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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