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 1988
| Updated in 1996