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?