MathGroup Archive 1999

[Date Index] [Thread Index] [Author Index]

Search the Archive

Tough Integral


In [mg20262] Tough Integral, Lawrence Walker wrote:

> Mathematica is able to calculate the following integral.
> In[1]:=
> Integrate[x^3/(E^x-1),{x,0,Infinity}]
> Out[1]=
> Pi^4/15
> For the life of me, I cannot solve this by hand.  Does any
> know or has any ideas.

It is well known that for Re[s]>1
Integral of x^(s-1) / (Exp[x]-1)dx from 0 to Infinity  = Gamma[s]
Zeta[s]
To do this by hand, write
        1/(Exp[x]-1) = Exp[-x][1 + Exp[-x] + Exp[-2x]+.....]
and use integration by parts. Mathematica gives the same result.

Ranko



  • Prev by Date: Re: dummy index list
  • Next by Date: Graphics inconsistencies
  • Previous by thread: Tough Integral
  • Next by thread: Re: Tough Integral