Did schrieb: > > With MMA 126.96.36.199, trying: > N[JacobiAmplitude[1 + I*2, 3/4], 20] > I get: > 1.3306295147276587227 - 0.8831325397142208140 I > > The equivalent with Maple 16: > evalf( JacobiAM( 1 + I*2 , sqrt(3/4) ), 20); > gives: > 1.8109631388621345158 + 0.88313253971422081404*I > > Which one, if any, is correct?
The Mathematica and Maple answers are closely related: Re1 = pi - Re2, Im1 = - Im2. This function has infinitely many branch points, and the two systems appear to prefer different branches. However, I am having trouble with the verification on Derive:
ELLIPTIC_F(phi, m) := INT(1/SQRT(1 - m*SIN(t_*phi)^2), t_, 0, 1)