[en] The longitudinal response function for a thermal electron gas was calculated including two quantum effects exactly, degeneracy and the quantum recoil. The Fermi-Dirac distribution was expanded in powers of a parameter that is small in the non-degenerate limit and the response function was evaluated in terms of the conventional plasma dispersion function to arbitrary order in this parameter. The infinite sum was performed in terms of poly logarithms in the long-wavelength and quasi-static limits, giving results that apply for arbitrary degeneracy. The results were applied to the dispersion relations for Langmuir waves and to screening, reproducing known results in the non-degenerate and completely degenerate limits], and generalizing them to arbitrary degeneracy. The occupation number for the completely degenerate limit is shown. The importance of the results regarding to semiconductor plasmas were highlighted. (orig./A.B.)