cauchy principal value double integral

*To*: mathgroup at smc.vnet.net*Subject*: [mg128834] cauchy principal value double integral*From*: Alex Krasnov <akrasnov at eecs.berkeley.edu>*Date*: Thu, 29 Nov 2012 06:06:26 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net

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