[en] An extension of the Feynman's path integral treatment for polaron ground state energy to an electron moving in D-dimension is obtained for the entire range of electron-phonon coupling constant. For this aim we used the method of equivalent representation of functional integrals suggested by us earlier. In our approach the leading term of polaron self-energy gives an upper bound of polaron ground state energy and represents an improvement over the known Feynman's variational estimation. New result of this paper is also the obtained all-coupling second correction to the leading term, which slightly lowers the polaron energy. Obtained results are in good agreement with known published data. (author). 39 refs, 2 figs, 6 tabs