  Previous analytical studies of quantum electrodynamics in $2+1$ dimensions
(QED3) have shown the existence of a critical number of fermions for onset of
chiral symmetry breaking, the most known being the value $N_c\approx3.28$
obtained by Nash to $1/N^2$ order in the $1/N$ expansion [16]. This analysis is
reconsidered by solving the Dyson-Schwinger equations for the fermion
propagator and the vertex to show that the more accurate gauge independent
value is $N_c\approx2.85$, and for $N<N_c$ the chiral symmetry is dynamically
broken. An estimate for the value of chiral condensate
$\langle\bar\psi\psi\rangle$ is given for $N=2$. Knowing precise $N_c$ would be
important for comparison between continuum studies and lattice simulations of
QED3.
