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MathGroup Archive 2005

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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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