Re: Question on PrincipalValue in Integrate

*To*: mathgroup at smc.vnet.net*Subject*: [mg80702] Re: Question on PrincipalValue in Integrate*From*: dimitris <dimmechan at yahoo.com>*Date*: Wed, 29 Aug 2007 04:19:29 -0400 (EDT)*References*: <fb0u04$j8r$1@smc.vnet.net>

On 28 =C1=FD=E3, 13:39, "Jung-Tsung Shen" <jus... at gmail.com> wrote: > A question on the "PrincipalValue" in the option of the command, Integrat= e: > > 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? In[12]:= $Version Integrate[1/(y - x), {x, -d, d}, PrincipalValue -> True, Assumptions - > Element[y,Reals] && d > 0] PiecewiseExpand[%] Out[12]= "5.2 for Microsoft Windows (June 20, 2005)" Out[13]= If[d <= y || y <= 0, -Log[-d + y] + Log[d + y], Integrate[1/(-x + y), {x, -d, d}, Assumptions -> y > 0 && d > y, PrincipalValue -> True]] Out[14]= Piecewise[{{-Log[d - y] + Log[d + y], d - y > 0 && y > 0}}, -Log[-d + y] + Log[d + y]] Cheers Dimitris PS It is high time we both upgrade!