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Re: cauchy principal value double integral

  • To: mathgroup at smc.vnet.net
  • Subject: [mg128915] Re: cauchy principal value double integral
  • From: daniel.lichtblau0 at gmail.com
  • Date: Tue, 4 Dec 2012 04:09:30 -0500 (EST)
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On Monday, December 3, 2012 2:18:53 AM UTC-6, Alex Krasnov wrote:
> I am unclear how to interpret the following result (Mathematica 8.0.4):
> 
> 
> 
> In:	Integrate[1/(x^2+y^2), {x, -1, 1}, {y, -1, 1}, PrincipalValue -> True]
> 
> Out:	-4*Catalan
> 
> 
> 
> How is Cauchy principal value defined in this case? Since the integrand is 
> 
> circularly symmetric around (0,0), excluding a shrinking neighborhood 
> 
> around (0,0) is not useful. Perhaps this result is merely an issue with 
> 
> option handling for multiple integrals?
> 
> 
> 
> Alex

That does indeed look like a bug.

Daniel Lichtblau
Wolfram Research



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