This is documentation for Mathematica 3, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.2)
 Documentation / Mathematica / Built-in Functions / Mathematical Functions / Elliptic Integrals  /
EllipticK

  • EllipticK[ m ] gives the complete elliptic integral of the first kind .
  • Mathematical function (see Section A.3.10).
  • EllipticK is given in terms of the incomplete elliptic integral of the first kind by .
  • See Section 3.2.11 for a discussion of argument conventions for elliptic integrals.
  • EllipticK[ m ] has a branch cut discontinuity in the complex m plane running from to .
  • See the Mathematica book: Section 3.2.11.
  • See also: JacobiZeta, EllipticNomeQ.

    Further Examples

    The complete elliptic integral of the first kind, , is a particular case of the hypergeometric function.

    In[1]:=

    Out[1]=

    This is the derivative.

    In[2]:=

    Out[2]=

    The function has a singularity at .

    Evaluate the cell to see the graph.

    In[3]:=