In external Compton scenario , we investigate the formation of the very hard electron spectrum in the fast-cooling regime , using a time-dependent emission model .
It is shown that a very hard electron distribution N ^ { \prime } _ { e } ( { \gamma ^ { \prime } } ) \propto { \gamma ^ { \prime } } ^ { - p } with the spectral index p \sim 1.3 is formed below the minimum energy of injection electron when inverse Compton scattering takes place in the Klein-Nishina regime , i.e. , inverse Compton scattering of relativistic electrons on broad-line region radiation in flat spectrum radio quasars .
This produces a very hard gamma-ray spectrum , and can reasonably explain the very hard Fermi -LAT spectrum of the flat spectrum radio quasar 3C 279 during the extreme gamma-ray flare in 2013 December .