Number of thermal photons

[Shackleford]

I'm not sure how to evaluate this integral.

http://i111.photobucket.com/albums/n149/camarolt4z28/IMG_20110317_145314.jpg?t=1300391815

http://i111.photobucket.com/albums/n149/camarolt4z28/IMG_20110317_145259.jpg?t=1300391802

[fzero]

This integral is a polylogarithm \text{Li}_3(1)=\zeta(3), the Riemann zeta function. http://en.wikipedia.org/wiki/Polylogarithm#Integral_representations http://en.wikipedia.org/wiki/Polylogarithm#Relationship_to_other_functions

The specific value of the zeta function can be found here: http://en.wikipedia.org/wiki/Riemann_zeta_function#Specific_values

[Shackleford]

Thanks. I had to rearrange and solve for just the integral, which is 2.404, and use that to show what N equals.