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In external Compton scenario, we investigate the formation of the very hardelectron spectrum in the fast-cooling regime, using a time-dependent emissionmodel. It is shown that a very hard electron distribution $N'_{\rme}(\gp)\propto\gp^{-p}$ with the spectral index $p\sim1.3$ is formed below theminimum energy of injection electron when inverse Compton scattering takesplace in the Klein-Nishina regime, i.e., inverse Compton scattering ofrelativistic electrons on broad-line region radiation in flat spectrum radioquasars. This produces a very hard gamma-ray spectrum, and can reasonablyexplain the very hard \emph{Fermi}-LAT spectrum of the flat spectrum radioquasar 3C 279 during the extreme gamma-ray flare in 2013 December.

Formation of very hard electron and gamma-ray spectra of flat spectrum radio quasar in fast-cooling regime