  The dynamical mean-field method is used to formulate a computationally
tractable theory of electron-phonon interactions in systems with arbitrary
local electron-electron interactions in the physically relevant adiabatic limit
of phonon frequency small compared to electron bandwidth or interaction scale.
As applications, the phonon contribution to the effective mass of a carrier in
a lightly doped Mott insulator is determined and the phase separation boundary
is discussed.
