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.