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MathGroup Archive 2005

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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


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