We calculate the interaction and excess free energies of the electron system at finite temperatures on the basis of the Singwi-Tosi-Land-Sj\"olander approximation [Phys. Rev. 176, 589 (1968)]. The results are parametrized in the form of analytic formulas, which adequately describe the equation of state for homogeneous, paramagnetic electron liquids over a wide range of the density and temperature parameters.
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Tanaka et al. (1985) studied this question.
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