Re: Wolfram, meet Stefan and Boltzmann

• To: mathgroup at smc.vnet.net
• Subject: [mg117277] Re: Wolfram, meet Stefan and Boltzmann
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Sun, 13 Mar 2011 05:29:03 -0500 (EST)

```
On 12 Mar 2011, at 11:10, AES wrote:

> No complaints here, just curious:
>
> Opened my copy of Mathematica 8.0 on my MacBook running Snow Leopard,
> and as my first action typed in and evaluated the famous integral
>
>      Timing[Integrate[x^3 /(Exp[x]-1),{x,0,Infinity}]]
>
> It took 19.8 seconds to get the famous result Pi^4 / 15.
>
> Seems a bit long -- what might have been taking up the time?
>

19.8 seconds seems a little slow:

In[1]:= Timing[Integrate[x^3/(Exp[x] - 1), {x, 0, Infinity}]]

Out[1]= {1.7872850000000005, Pi^4/15}

or

In[1]:= v = Timing[Integrate[x^3/(Exp[x] - 1), x]]

Out[1]= {0.05884400000000001, 3*x^2*PolyLog[2, E^x] -
6*x*PolyLog[3, E^x] + 6*PolyLog[4, E^x] - x^4/4 +
x^3*Log[1 - E^x]}

In[2]:= Timing[Limit[v, x -> Infinity] - Limit[v, x -> 0]]
Out[2]= {1.778428, {0., Pi^4/15}}

The sum of the last two timings is almost exactly equal the first one.

Andrzej Kozlowski

```

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