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

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Alex Krasnov

Posts: 15
Registered: 10/3/12
cauchy principal value double integral
Posted: Dec 3, 2012 3:18 AM
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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




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