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Re : Principal Value integral

• To: mathgroup at smc.vnet.net
• Subject: [mg52373] Re : [mg52361] Principal Value integral
• From: "Jaccard Florian" <Florian.Jaccard at he-arc.ch>
• Date: Thu, 25 Nov 2004 05:49:44 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

Hello Carlo,

I obtain the correct answer with 5.0 !
What version do you use?

In fact, we always should be very prudent using Integrate, because there are still a lot of bugs. Just look in the archive!
A good thing is always to check that NIntegrate gives the same numerical value!

Regards
 
F.Jaccard


-----Message d'origine-----
De : Carlo Teubner [mailto:AskMeAndIllTellYou. at example.com] 
Envoyé : mercredi, 24. novembre 2004 08:33
À : mathgroup at smc.vnet.net
Objet : [mg52361] Principal Value integral

The following Principal Value integral does not appear to give the 
correct result.

Integrate[1/(x^3-1), {x, -Infinity, Infinity}, PrincipalValue->True]

This gives I Pi / 3, which surely can't be right since the answer should 
be real.

When doing it numerically, it gives the right answer:

<<NumericalMath`CauchyPrincipalValue`
CauchyPrincipalValue[1/(x^3-1), {z, -Infinity, {1}, Infinity}]

This gives -1.8138 which is the correct answer (it's -Pi/Sqrt[3]).

Any explanations? Is this a bug or am I missing something?

Carlo