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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)
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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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