Re: Principal Value integral
- To: mathgroup at smc.vnet.net
- Subject: [mg52395] Re: [mg52361] Principal Value integral
- From: DrBob <drbob at bigfoot.com>
- Date: Thu, 25 Nov 2004 05:50:53 -0500 (EST)
- References: <200411240732.CAA28890@smc.vnet.net>
- Reply-to: drbob at bigfoot.com
- Sender: owner-wri-mathgroup at wolfram.com
Version 5.1 gets your desired result:
Integrate[1/(x^3 - 1), {x, -Infinity, Infinity},
PrincipalValue -> True]
-(Pi/Sqrt[3])
Bobby
On Wed, 24 Nov 2004 02:32:35 -0500 (EST), Carlo Teubner <"AskMeAndIllTellYou."@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.
>
> 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
>
>
>
>
--
DrBob at bigfoot.com
www.eclecticdreams.net
- References:
- Principal Value integral
- From: Carlo Teubner <AskMeAndIllTellYou.@example.com>
- Principal Value integral