This is documentation for Mathematica 3, which was
based on an earlier version of the Wolfram Language.
 EllipticE EllipticE[ m ] gives the complete elliptic integral . EllipticE[, m ] gives the elliptic integral of the second kind . Mathematical function (see Section A.3.10). For , . . See SectionÂ 3.2.11 for a discussion of argument conventions for elliptic integrals. EllipticE[ m ] has a branch cut discontinuity in the complex m plane running from to . EllipticE[, m ] has a branch cut discontinuity running along the ray from to infinity. See the Mathematica book: Section 3.2.11. See also: JacobiZeta, JacobiAmplitude. Further Examples This is the definition of the elliptic integral of the second 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 second kind, a particular case of the hypergeometric function. In[2]:= Out[2]= This is the indefinite integral of the complete integral . In[3]:= Out[3]= This is a series expansion around . In[4]:= Out[4]= This is the derivative of the incomplete function with respect to . In[5]:= Out[5]=