gives the complete elliptic integral .

gives the elliptic integral of the second kind .


  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • For , .
  • .
  • EllipticE[m] has a branch cut discontinuity in the complex m plane running from to .
  • EllipticE[ϕ,m] has a branch cut discontinuity running along the ray from to infinity.
  • For certain special arguments, EllipticE automatically evaluates to exact values.
  • EllipticE can be evaluated to arbitrary numerical precision.
  • EllipticE automatically threads over lists.
Introduced in 1988
| Updated in 1996