We investigate the Holstein model, which describes the coupling of a local phonon mode to a band of conduction electrons, in d=\infty . In the limit of large phonon frequency \omega ₀, this model can be mapped onto a Hubbard model with effective attractive electron--electron interaction. The latter model is known to exhibit a metal--insulator transition at half filling for large enough coupling strengths. We show that the system with small phonon frequencies also develops a gap as function of the electron--phonon coupling. The physics of the gap formation differs for small and large phonon frequencies, e.g. the ``hysteresis'' seen for large \omega ₀ disappears for smaller values.

PACS numbers: 71.10.Fd, 71.30.+h, 71.38.--k