Mean photon energy
= Mean photon energy
{title2=$\langle E_\gamma\rangle=\frac{\pi^4}{30\zeta(3)}T\simeq2.701T$}
The number and energy integrals of a zero-chemical-potential <photon> gas give $n=2\zeta(3)T^3/\pi^2$ and $\rho=\pi^2T^4/15$ in <natural units>. Their ratio is the mean energy per <photon>. It is useful for converting a relic number-density ratio into an energy-density ratio.