Re: Bug in Integrate in Version 5.1?

*To*: mathgroup at smc.vnet.net*Subject*: [mg56782] Re: [mg56737] Bug in Integrate in Version 5.1?*From*: Bob Hanlon <hanlonr at cox.net>*Date*: Fri, 6 May 2005 02:59:49 -0400 (EDT)*Reply-to*: hanlonr at cox.net*Sender*: owner-wri-mathgroup at wolfram.com

Here is a workaround $Version 5.1 for Mac OS X (January 27, 2005) a=Integrate[x^3/(Exp[x]-1),{x,0,Infinity}] Pi^4/15 b=Limit[ Integrate[-3 x^2 Log[1-Exp[-x]],{x,0,x1}], x1->Infinity] Pi^4/15 Bob Hanlon > > From: A.Reischl at gmail.com To: mathgroup at smc.vnet.net > Date: 2005/05/05 Thu AM 06:01:20 EDT > Subject: [mg56782] [mg56737] Bug in Integrate in Version 5.1? > > Hello, > > Integrate gives the following answer for this integral: > > a = Integrate[x^3 /(Exp[x] - 1), {x, 0, Infinity}] > N[a] > > Out[1]= Pi^4/15 > Out[2]= 6.49394 > > which I think is correct. > This integral, which should be the same ( by partial integration), > gives: > b = Integrate[-3 x^2 Log[1 - Exp[-x]], {x, 0, Infinity}] > N[b] > > Out[3]= (11*Pi^4)/60 > Out[4]= 17.8583 > > while numerical integration gives: > NIntegrate[-3x^2 Log[1 - Exp[-x]], {x, 0, Infinity}] > Out[5]= 6.49394 > > This is done with version 5.1. > > Version 4.2 gives > c=Integrate[-3*x^2*Log[1 - Exp[-x]], {x, 0, Infinity}] > N[c] > > Out[1]= Pi^4/15 > Out[2]= 6.49394 > > (Remarkably version 4.2. complaints: "Series::esss: Essential > singularity > encountered in ..." while calculating the correct result. ) > > So the result in version 5.1. looks wrong. > Or did I make a mistake? > > Cheers > Alexander > >