EllipticF

EllipticF[ϕ,m]

gives the elliptic integral of the first kind .

Details

  • 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.

Examples

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Basic Examples  (2)

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Scope  (7)

Generalizations & Extensions  (1)

Applications  (5)

Properties & Relations  (6)

Possible Issues  (2)

Neat Examples  (2)

See Also

EllipticK  EllipticE  EllipticPi  JacobiZeta  JacobiAmplitude

Tutorials

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