1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Integration problem to calculate partition function of a gase in a blackbody

  1. Jan 11, 2009 #1
    1. The problem statement, all variables and given/known data
    This is the integration i have to solve
    I=[tex]\int x^{2}In(1-exp(-ax))dx[/tex]
    integration is from zero to infinity

    3. The attempt at a solution
    I know that it should be solved with integration by parts
    du=[a exp(-ax)] / [1-exp(-ax)]
    v=x[tex]^{3}[/tex] /3
    when i put this into the integration formula
    I=u*v-[tex]\int v*du[/tex]
    it becomes more complicated
    I=In(1-exp(-ax))*x[tex]^{3}[/tex]/3 - [tex]\int dx * (x^3/3) * [a exp(-ax)] / [1-exp(-ax)][/tex]
    so what should i do after this , i can't figure it out, am i doing it wrong?
  2. jcsd
  3. Jan 11, 2009 #2
    Use Gamma function and expand integrand using geometric series.
  4. Jan 11, 2009 #3
    if i do that i should calculate the series from zero to infinity. when will i know that i should stop?
  5. Jan 11, 2009 #4
    You should get some good looking series at the end, and you can get a closed form expression. Usually, one ends up with some kind of zeta functions.

    You might get things like:
    [tex]\sum \frac{1}{n^2}=\frac{\pi^2}{6}[/tex]

    [tex]\sum \frac{1}{n^4}=\frac{\pi^4}{90}[/tex]

    which can be simplified by consulting some tables.
  6. Jan 11, 2009 #5
    well thank you for your help. now i will give it a try.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Integration problem to calculate partition function of a gase in a blackbody
  1. Partition function (Replies: 2)