The single-polaron band structure of the Holstein model in one and two
dimensions is studied using resummed strong-coupling perturbation the
ory. Well-converged results are obtained for phonon frequencies of the
order of the hopping integral and strong-to-intermediate electron-pho
non coupling. The polaron band structure at intermediate coupling is s
hown to deviate markedly from that of a nearest-neighbor tight-binding
model and is in fact similar in shape to the prediction of weak-coupl
ing self-consistent perturbation theory.