Non-perturbative production of fermions after chaotic inflation has been th
e object of several studies in the very recent past. However, the results i
n the most interesting case of production of massive fermions in an expandi
ng Universe were so far known only numerically. We provide very simple and
readable analytical formulae, both for the spectra of the created fermions
and for their total energy density. Their derivation is closely related to
the one adopted for bosons and exploits the fact that the production occurs
during very short intervals of non-adiabatical change of the fermionic fre
quency. Our formulae show the presence of resonance bands if the expansion
of the Universe is neglected, and their disappearance when the latter is in
cluded. As in the bosonic case, this last effect is due to the stochastic c
haracter that the expansion gives to the whole process. Backreaction is con
sidered in the last part of the work. All our analytical results are in exc
ellent agreement with the previous numerical ones in the regime of validity
of the latter. However, a more accurate scaling for the energy density of
the produced fermions is here found.