Re: Bug in Integrate in Version 5.1?

*To*: mathgroup at smc.vnet.net*Subject*: [mg56810] Re: [mg56737] Bug in Integrate in Version 5.1?*From*: Chris Chiasson <chris.chiasson at gmail.com>*Date*: Fri, 6 May 2005 03:01:01 -0400 (EDT)*References*: <200505051001.GAA21888@smc.vnet.net>*Reply-to*: Chris Chiasson <chris.chiasson at gmail.com>*Sender*: owner-wri-mathgroup at wolfram.com

Maybe they smoked some of their sums and improper definite integrals with that change in the output of the limit command. A "hunch" from a previous thread: (The integration is correct in 5.0 (happy happy joy joy), so I don't know if this will work for you) Limit[Integrate[-3*x^2*Log[1-Exp[-x]],{x,a,Infinity}],a->0] Regards, On 5/5/05, A.Reischl at gmail.com <A.Reischl at gmail.com> wrote: > 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 > > -- Chris Chiasson http://chrischiasson.com/ 1 (810) 265-3161

**References**:**Bug in Integrate in Version 5.1?***From:*A.Reischl@gmail.com