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Integral in Stefan-Boltzmann law

  1. Mar 21, 2010 #1

    I'm wondering if anybody can recommend me a book where it's explained how to solve (analytically) integral that appears in Stefan-Boltzmann's law:

    [tex]\int_0^\infty \frac{x^n}{(e^x-1)^m}dx[/tex]

  2. jcsd
  3. Mar 21, 2010 #2


    Staff: Mentor

    As far as I know it does not have an analytical solution.
  4. Mar 22, 2010 #3
    Well you consider the integral:
    [tex]\int_0^\infty \frac{\sin(kx)}{e^x-1}dx[/tex], we can use Taylor expansion on it and solve it via contour integration.

    At my class we solved that by using some kind of generating function [tex]F(p)=\int_0^\infty x^n \ln(1-e^{p-x})dx[/tex], then derived it by p and evaluated at p=0. First we expanded logarithm in Taylor series, and we got Riemann zeta function and Gamma function.

    But I was wondering if there are any books that show where this all comes from...
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