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Considering Hubbard models with infinite U, the leading terms of the electronic self-energy due to an on-site electron-phonon interaction are calculated within a 1/N expansion. In particular, the modifications of the Eliashberg function α 2 F (ω) due to strong correlations are described and calculated for a simple square lattice as a function of doping. We find that the on-site electron-phonon coupling is in general slightly enhanced in forward scattering but dramatically suppressed for scattering with large momentum transfers by correlations. This implies at least in the single-band case that the electron-phonon coupling is greatly reduced in transport quantities and to a much smaller degree in α 2 F because of electronic correlations.