  According to recent Quantum Monte Carlo simulations the small polaron theory
is practically exact in a wide range of the long-range (Frohlich)
electron-phonon coupling and adiabatic ratio. We apply the Lang-Firsov
transformation to convert the strong-coupling term in the Hamiltonian into the
form of an effective hopping integral and derive the single-particle Green's
function describing propagation of the small Frohlich polaron. One and two
dimensional spectral functions are studied by expanding the Green's function
perturbatively. Numerical calculations of the spectral functions are produced.
Remarkably, the coherent spectral weight (Z) and effective mass (Z')
renormalisation exponents are found to be different with Z'>>Z, which can
explain a small coherent spectral weight and a relatively moderate mass
enhancement in oxides.
