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Topic: cauchy principal value double integral
Replies: 5   Last Post: Dec 6, 2012 4:56 AM

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daniel.lichtblau0@gmail.com

Posts: 20
Registered: 7/23/12
Re: cauchy principal value double integral
Posted: Dec 4, 2012 4:08 AM
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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]
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> Out: -4*Catalan
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>
>
> How is Cauchy principal value defined in this case? Since the integrand is
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> circularly symmetric around (0,0), excluding a shrinking neighborhood
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> around (0,0) is not useful. Perhaps this result is merely an issue with
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> option handling for multiple integrals?
>
>
>
> Alex


That does indeed look like a bug.

Daniel Lichtblau
Wolfram Research




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