= Angular-frequency Planck energy density
{title2=$u_\omega=\hbar\omega^3/[\pi^2c^3(e^{\hbar\omega/(k_BT)}-1)]$}
The bulk <photon> mode <density> per <volume> per <angular frequency> is $\omega^2/(\pi^2c^3)$, including two transverse polarizations. Multiply it by the thermal oscillator <energy> $\hbar\omega/(e^{\hbar\omega/(k_BT)}-1)$ to obtain the displayed spectrum. Its integral is $u=\pi^2k_B^4T^4/(15\hbar^3c^3)$. This is <volume> <energy> <density> rather than <radiance> or surface exitance; isotropic equilibrium radiation has outward black-surface flux $cu/4$. <zero-point energy> is excluded from this thermal spectrum.
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