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MathGroup Archive 2007

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Re: Question on PrincipalValue in Integrate

  • To: mathgroup at smc.vnet.net
  • Subject: [mg80696] Re: Question on PrincipalValue in Integrate
  • From: "David W.Cantrell" <DWCantrell at sigmaxi.net>
  • Date: Wed, 29 Aug 2007 04:16:23 -0400 (EDT)
  • References: <fb0u04$j8r$1@smc.vnet.net>

"Jung-Tsung Shen" <jushen at gmail.com> wrote:
> 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?

Using version 5.2:

In[5]:=
Assuming[0 < y < d, Integrate[1/(y-x), {x, -d, d}, PrincipalValue -> True]]

Out[5]=
- Log[d - y] + Log[d + y]

as desired.

David


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