Relativistic formulation for the Doppler-broadened line profile

Profiles of spectral lines due to the thermal motion of light-emitting particles are formulated based on the classical and the relativistic Doppler effects, respectively. For the classical case, the well-known Doppler-broadened line profile is reproduced. For the relativistic case, the line profile obtained is asymmetrically broadened with increasing temperature. However, the peak frequency remains unshifted, in contrast to blueshifted, as has been predicted in the current literature. Reasoning is given as to why the relativistic Doppler-broadened line profile currently accepted is probably invalid.