High-frequency asymptotics of one integral in the theory of equilibrium radiation of electron gas

It is considered an improper integral that determines the high-frequency asymptotics of the spectral energy distribution of equilibrium radiation in an ideal electron gas. It has been established that in the “high-frequency” limit the asymptotics of this integral has a power-law character, and its value is proportional to the density of the electron gas as a function of temperature and chemical potential for arbitrary degeneracy of electrons.