Principal Value integral
- To: mathgroup at smc.vnet.net
- Subject: [mg52361] Principal Value integral
- From: Carlo Teubner <AskMeAndIllTellYou. at example.com>
- Date: Wed, 24 Nov 2004 02:32:35 -0500 (EST)
- Organization: Oxford University, England
- Sender: owner-wri-mathgroup at wolfram.com
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
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