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MathGroup Archive 2004

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Re: Principal Value integral

  • To: mathgroup at smc.vnet.net
  • Subject: [mg52374] Re: Principal Value integral
  • From: "David W. Cantrell" <DWCantrell at sigmaxi.org>
  • Date: Thu, 25 Nov 2004 05:49:46 -0500 (EST)
  • References: <co1fcm$smm$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Carlo Teubner <AskMeAndIllTellYou. at example.com> wrote:
> 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.

Using version 5.0, the result is correct:  -Pi/Sqrt[3] .
What version are you using?

David

> 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


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