Date: Dec 3, 2012 3:18 AM
Author: Alex Krasnov
Subject: cauchy principal value double integral

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?