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