This is documentation for Mathematica 3, which was
based on an earlier version of the Wolfram Language.
 EllipticF EllipticF[, m ] gives the elliptic integral of the first kind . Mathematical function (see Section A.3.10). For , . The complete elliptic integral associated with EllipticF is EllipticK. EllipticF is the inverse of JacobiAmplitude. If then . EllipticF[, m ] has a branch cut discontinuity running along the ray from to infinity. See SectionÂ 3.2.11 for a discussion of argument conventions for elliptic integrals. See the Mathematica book: Section 3.2.11. See also: JacobiZeta, JacobiAmplitude. Further Examples This is the definition of the elliptic integral of the first kind. Classically, the integral is defined for on the interval , but the function also makes sense for more general (complex-valued) . In[1]:= Out[1]= Setting gives the complete elliptic integral of the first kind, which is traditionally denoted by a different letter, . In[2]:= Out[2]= These are the partial derivatives. In[3]:= Out[3]= In[4]:= Out[4]=