Spectral analysis of the first model (solid line) of Fig. 1. Upper panel: thermal SZE-21 cm for kT = 7 keV and τ = 5 × 10^-3 calculated with the relativistic approach (solid line) and the non-relativistic approach (dashed line), compared with the standard SZE calculated with the relativistic approach (long-dashed line) and the non-relativistic approach (dotted line). Middel panel: percentage difference between the relativistic result and the non-relativistic one. Lower panel: second derivative of the input spectrum.