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

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 did Posts: 80 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.

Date Subject Author
4/2/13 did
4/2/13 Nasser Abbasi
4/2/13 did
4/2/13 clicliclic@freenet.de
4/3/13 did
4/4/13 clicliclic@freenet.de
4/4/13 Waldek Hebisch
4/5/13 clicliclic@freenet.de
4/5/13 did
4/6/13 clicliclic@freenet.de
4/7/13 Waldek Hebisch
4/8/13 clicliclic@freenet.de
4/8/13 Waldek Hebisch
4/9/13 clicliclic@freenet.de
4/13/13 clicliclic@freenet.de
4/8/13 Axel Vogt
4/3/13 Joe keane