Integral in Stefan-Boltzmann law

[dingo_d]

Hi!

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:

$$\int_0^\infty \frac{x^n}{(e^x-1)^m}dx$$

Thanx!

 

[Dale]

As far as I know it does not have an analytical solution.

 

[dingo_d]

Well you consider the integral:
$$\int_0^\infty \frac{\sin(kx)}{e^x-1}dx$$, 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 $$F(p)=\int_0^\infty x^n \ln(1-e^{p-x})dx$$, 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...