Re: our good (?!) friend RootSum

*To*: mathgroup at smc.vnet.net*Subject*: [mg75078] Re: our good (?!) friend RootSum*From*: "dimitris" <dimmechan at yahoo.com>*Date*: Mon, 16 Apr 2007 20:11:28 -0400 (EDT)*References*: <evpoas$698$1@smc.vnet.net><evsqoi$119$1@smc.vnet.net>

Thanks a lot for interest. Faithfully Dimitris =CF/=C7 Michael Weyrauch =DD=E3=F1=E1=F8=E5: > Hello > > well, I think, at this stage, we just have to live with the fact that this > type of integrals is not evaluated correctly by Mathematica, but other CAS > -- if we like it or not-- do that easily. It 's up to the developers > to fix that. And I would be surprised if it wasn't fixed in the upcoming = version. > > You my find it interesting to also modify the Series command using > > Unprotect[Series]; > Series[a___] := Null /; (Print[series[a]]; False) > > and then integrate any of the integrals you discussed recently in your se= ries of threads on integration (including the one of this > thread). > >From the rather lengthy output (in Mathematica 5.2) we see the following: > > 1) Series[] is indeed explicitly called along the way expanding the antid= erivative around Infinity. > > 2) The RootSum[] is expanded out and Root objects are inserted explicitly= . So RootSum isn't the offender. > > 3) Internally the results are expressed by a new variable > > Integrate`NLtheoremDump`newx > > (Hopefully this is not meant to read as "Dump the Newton-Leibnitz theorem= " ;=), but at least we are definitly convinced now that the > NL theorem is used for integration.) > > 4) If you calculate the series expansion at Infinity using the output of = the above modification of Series you see that this also is > done correctly. If you just replace the variable Integrate`NLtheoremDump= `newx with Infinity in this output of Series[ ] the correct > limit 0 is obtained. So it appears that also Series[] is doing everthing = just fine. > > 5) Why Mathematica then doesn't finally use this easily obtained limit to= return the evaluated Integral remains mysterious to me. > > I suggest, let's wait and see that these somewhat mysterious effects will= disappear... > > Regards Michael