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Topic: Bug in Jacobian Amplitude?
Replies: 16   Last Post: Apr 13, 2013 1:35 PM

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Posts: 1,245
Registered: 4/26/08
Re: Bug in Jacobian Amplitude?
Posted: Apr 2, 2013 1:48 PM
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Did schrieb:
> With MMA, 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.


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