Bug in Integrate in Version 5.1?
- To: mathgroup at smc.vnet.net
- Subject: [mg56737] Bug in Integrate in Version 5.1?
- From: A.Reischl at gmail.com
- Date: Thu, 5 May 2005 06:01:20 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
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
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