Comparison of the different inverse-Compton spectra of a thermal soft photon field (T = 5780 K) scattering on a mono-energetic particle distribution of Lorentz factor γ = 1e2 with the relative errors in dot-dot-dashed thin lines. The numerically integrated spectra with the thermal distribution described by Planck’s law is shown in black. The analytically integrated spectra with the thermal distribution described by the modified Wien’s law (given by Eq. (21)) is shown in blue. As a comparison, we also provide the spectrum from Zdziarski & Pjanka (2013) in orange.