EllipticE

EllipticE[m]

gives the complete elliptic integral .

EllipticE[ϕ,m]

gives the elliptic integral of the second kind .

Details

  • 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.

Examples

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Basic Examples  (2)

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Scope  (14)

Generalizations & Extensions  (1)

Applications  (8)

Properties & Relations  (7)

Possible Issues  (2)

Neat Examples  (4)

See Also

EllipticK  EllipticF  EllipticPi  JacobiZeta  JacobiAmplitude

Tutorials

Introduced in 1988
(1.0)
| Updated in 1996
(3.0)