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
>
>