The Hubbard-Holstein model after canonical Lang-Firsov transformation
is investigated. Two peculiarities of the model are taken into account
: a) the strong electron correlations and b) the fact that the hopping
s of polarons between lattice sites are accompanied by an indefinite n
umber of phonons. A new diagram technique based on the classification
of irreducible many-particle Green functions or Kubo cumulants is deve
loped. Phonon renormalization of electronic functions is considered. A
theorem about connected vacuum diagrams is established, and Dyson equ
ation for electron Green function is obtained.