The effect of inverse Compton scatterings in Klein-Nishina regime on the fast cooling synchrotron spectrum. The normalized synchrotron spectrum defined by is plotted as a function of the normalized frequency ν/ν_m, as well as the corresponding photon index dlnu_ν/dlnν − 1. All spectra in thick solid line are computed numerically using a detailed radiative code including synchrotron radiation and inverse Compton scatterings (see text). Spectra in thin dotted line are computed with synchrotron radiation only. For clarity purposes, all other processes (adiabatic cooling, synchrotron self-absorption, γγ annihilation) are neglected. A ratio Γ_c/Γ_m = 10^-6 is assumed to ensure that all electrons are in fast cooling regime. The maximum Lorentz factor of electrons is fixed to Γ_max = 10⁴ Γ_min so the high energy cutoff in the synchrotron spectrum appears at the same frequency in all cases plotted here. The four panels correspond to increasing values of the w_m parameter, w_m = 0.01, 1, 100 and 10⁴ from the top-left to the bottom-right panel, i.e. to a growing importance of Klein-Nishina corrections for inverse Compton scatterings. In each panel, the six curves in solid line correspond to increasing values of the Y_Th parameter, Y_Th = 0.1, 1, 10, 10², 10³ and 10⁴, i.e. to a growing efficiency of inverse Compton scatterings. The table inserted in each panel lists the values of the ratio ℰ_ic/ℰ_syn of the inverse Compton component (not plotted here) over the synchrotron component. In the bottom-left panel (w_m = 100), the synchrotron spectrum obtained assuming a slow injection over t_ex (see text) is also plotted in dashed line for comparison.