
Re: Bug in Jacobian Amplitude?
Posted:
Apr 2, 2013 1:48 PM


Did schrieb: > > With MMA 9.0.1.0, 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)
ELLIPTIC_F(1.3306295147276587227  0.883132539714220814*#i, 3/4)
0.99660789047167089453  0.36927172197460334749*#i
This integral doesn't look like 1 + 2*#i. What is wrong here?
Along the same linear integration path from 0 to the Maple value, the integrand passes though a branch cut of the square root, and I haven't tried to work around this.
Martin.

