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