Landau-Khalatnikov-Fradkin transformation of the fermion propagator in massless reduced QED

We study the gauge-covariance of the massless fermion propagator in reduced quantum electrodynamics (QED). Starting from its value in some gauge, we evaluate an all order expression for it in another gauge by means of the Landau-Khalatnikov-Fradkin transformation. We find that the weak-coupling expansions thus derived are in perfect agreement with the exact calculations. We also prove that the fermion anomalous dimension of reduced QED is gauge invariant to all orders of perturbation theory except for the first one.