Abstract
Temperature-dependent behavior of the electron gas is evaluated by a new method which does not require the restriction of the Sommerfeld method. Our method is based on the observation that the Fermi distribution function generates an infinite number of poles in the complex plane at finite temperature. This formalism is applied to derive the free-electron susceptibilities $\ensuremath{\chi}(r)$ and $\ensuremath{\chi}(q)$ in three dimensions analytically where the Sommerfeld expansion is not applicable. Finally, it is demonstrated that our method produces the identical result with the one obtained by the Sommerfeld method in the evaluation of the thermodynamic energy of the electron gas.
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