JacobiAmplitude

JacobiAmplitude[u,m]

gives the amplitude for Jacobi elliptic functions.

Details

  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • JacobiAmplitude[u,m] converts from the argument u for an elliptic function to the amplitude ϕ.
  • JacobiAmplitude is the inverse of the elliptic integral of the first kind. If , then .
  • For certain special arguments, JacobiAmplitude automatically evaluates to exact values.
  • JacobiAmplitude can be evaluated to arbitrary numerical precision.
  • JacobiAmplitude automatically threads over lists.

Examples

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Basic Examples  (3)

Evaluate numerically:

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Series expansion about the origin:

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Scope  (6)

Generalizations & Extensions  (1)

Applications  (5)

Properties & Relations  (4)

Possible Issues  (1)

See Also

EllipticE  EllipticF

Tutorials

Introduced in 1988
(1.0)