Elliptic function -- different definitions Hi, I have recently discovered, that the definition of the complete elliptic integral of the first kind in Wolfram Mathematica (EllipticK[m]) is different from the usual (K(m)), given in Abramowitz-Stegun. Their domains are not the same. In Abramowitz-Stegun, K is defined for |m| < 1, however in Mathematica, the domain is -Infinity < m<1. My question is, the following. How EllipticK[m] is related to K, when m < -1? Is it related at all?