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MathGroup Archive 2007

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Question on PrincipalValue in Integrate

  • To: mathgroup at smc.vnet.net
  • Subject: [mg80672] Question on PrincipalValue in Integrate
  • From: "Jung-Tsung Shen" <jushen at gmail.com>
  • Date: Tue, 28 Aug 2007 06:38:57 -0400 (EDT)

A question on the "PrincipalValue" in the option of the command, Integrate:

Mathematica (v5.0 Mac) gives the following command

Integrate[1/(y-x), {x, -d, d}, PrincipalValue -> True]

the answer


If[y > 0 && y < d, I Pi - Log[d - y] + Log[d + y], Integrate[1/(-x +
y), {x, -d, d}, Assumptions -> d ? y || y ? 0]]

But shouldn't the first part of the answer by - Log[d - y] + Log[d +
y], without the I Pi? This can be computed using the very definition
of the principal value.

Any comments are greatly appreciated.

Thanks.

JT

PS. Recently I have found several verified bugs in v5.0. Maybe it's
time to upgrade to v6.0?


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