Relativistic correction of $(v/c)^{2}$ to the collective Thomson scattering

Collective Thomson scattering with inclusion of relativistic correction of $(v/c)^{2}$ is theoretically investigated. The correction is rather small when inferring plasma parameters from the spectra off thermal electron plasma waves in the plasmas. Since the full formula of the corrected result is rather complicated, a simplified one is derived for the sake of practical use, which agrees well with the un-simplified one.