       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

(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= Pi^4/15
> Out= 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= (11*Pi^4)/60
> Out= 17.8583
>
> while numerical integration gives:
> NIntegrate[-3x^2 Log[1 - Exp[-x]], {x, 0, Infinity}]
> Out= 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= Pi^4/15
> Out= 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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