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.

Jacobi Elliptic Functions

Inverse Jacobi Elliptic Functions

Weierstrass Elliptic Functions

Inverse Weierstrass Elliptic Functions

Theta Functions

Elliptic Exponential Functions

(RefLink[JacobiAmplitude, paclet:ref/JacobiAmplitude]) — convert from argument u and parameter m to amplitude ϕ

(RefLink[EllipticNomeQ, paclet:ref/EllipticNomeQ]) — convert from parameter m to nome q

(RefLink[InverseEllipticNomeQ, paclet:ref/InverseEllipticNomeQ]) — convert from nome q to parameter m

(RefLink[WeierstrassInvariants, paclet:ref/WeierstrassInvariants]) — convert from half-periods to invariants

(RefLink[WeierstrassHalfPeriods, paclet:ref/WeierstrassHalfPeriods]) — convert from invariants to half-periods