EllipticF

EllipticF[, m] gives the elliptic integral of the first kind .

Mathematical function (see Section A.3.10).

For , .

The complete elliptic integral associated with EllipticF is EllipticK.

EllipticF is the inverse of JacobiAmplitude. If then .

EllipticF[, m] has a branch cut discontinuity running along the ray from to infinity.

See Section 3.2.11 for a discussion of argument conventions for elliptic integrals.

See The Mathematica Book: Section 3.2.11.

See also: JacobiZeta, JacobiAmplitude.

Further Examples