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 Documentation / Mathematica / Built-in Functions / Mathematical Functions / Elliptic Functions  /
JacobiAmplitude

  • JacobiAmplitude[ u , m ] gives the amplitude for Jacobi elliptic functions.
  • Mathematical function (see Section A.3.10).
  • JacobiAmplitude[ u , m ] converts from the argument for an elliptic function to the amplitude .
  • JacobiAmplitude is the inverse of the elliptic integral of the first kind. If , then .
  • See the Mathematica book: Section 3.2.11Section 3.2.11.

    Further Examples

    When the modulus is a real number in the interval , JacobiAmplitude is inverse to EllipticF (both being considered as functions of the first argument).

    In[1]:=

    Out[1]=

    This is the derivative.

    In[2]:=

    Out[2]=

    This is a series expansion around .

    In[3]:=

    Out[3]=