did
Posts:
77
Registered:
9/14/05


Re: Bug in Jacobian Amplitude?
Posted:
Apr 3, 2013 3:22 AM


Hi Martin,
Of course I expected a problem with branch cut. From my Byrd & Friedman I tried the (supposed) two equivalent definitions:
N[JacobiAmplitude[1+I*2, 3/4], 20] 1.3306295147276587227  0.8831325397142208140 I
N[ArcTan[JacobiCN[1+I*2, 3/4] , JacobiSN[1+I*2, 3/4]], 20] 1.8109631388621345158 + 0.8831325397142208140 I
and the Maple equivalent: evalf(JacobiAM(1+I*2,sqrt(3/4)),20); evalf(arctan(JacobiSN(1+I*2,sqrt(3/4)),JacobiCN(1+I*2,sqrt(3/4))),20); 1.8109631388621345158 + 0.88313253971422081406 I 1.8109631388621345158 + 0.88313253971422081409 I
So Maple is consistent and matches MMA second expression. Why MMA should have a different definition of JacobiAmplitude? But, why it seems OK for other values? e.g. N[JacobiAmplitude[1 + I/2, 3/4], 20] 0.94644250288672303746 + 0.36465966602260927458 I N[ArcTan[JacobiCN[1 + I/2, 3/4], JacobiSN[1 + I/2, 3/4]], 20] 0.94644250288672303746 + 0.36465966602260927458 I
Did
On Tuesday, 2 April 2013 19:48:53 UTC+2, clicl...@freenet.de wrote: > 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.

