  The QED Dyson-Schwinger equation for the photon-fermion one-particle
irreducible Green function, the photon-fermion vertex, is investigated using a
Ball-Chiu description for its longitudinal part, together with the
K{\i}z{\i}lersu-Reenders-Pennington basis for its transverse part. Exact
expressions for all the transverse form factors are derived from the vertex
Dyson-Schwinger equation. Furthermore, feeding the Dyson-Schwinger equation
with a simplified vertex that goes beyond the perturbative solution, some of
the results of the one-loop perturbative calculation are recovered in a more
general framework. The approach allows also exact results for the on-shell
vertex, that encode the anomalous magnetic and electric fermion couplings, and
for its soft photon limit. The investigation of the chiral limit of the
photon-fermion vertex shows that a limited number of transverse form factors
are required, a result that, once more, is in good agreement with a one-loop
calculation for QED but that appears in a more general framework. The results
derived for the photon-fermion vertex can be extended easily to the quark-gluon
vertex after proper modifications.
