gives the elliptic integral of the first kind .
- Mathematical function, suitable for both symbolic and numerical manipulation.
- For , .
- The complete elliptic integral associated with EllipticF is EllipticK.
- EllipticF is the inverse of JacobiAmplitude. If then .
- EllipticF[ϕ,m] has a branch cut discontinuity running along the ray from to infinity.
- For certain special arguments, EllipticF automatically evaluates to exact values.
- EllipticF can be evaluated to arbitrary numerical precision.
- EllipticF automatically threads over lists.
Introduced in 1988Updated in 1996