  Within the self-consistent Hartree-Fock approximation, an explicit expression
for the ground state energy of inhomogeneous Bose gas is derived as a
functional of the inhomogeneous density of the Bose-Einstein condensate. The
results obtained are based on existence of the off-diagonal long-range order in
the single-particle density matrix for systems with a Bose-Einstein condensate.
This makes it possible to avoid the use of anomalous averages. The explicit
form of the kinetic energy, which differs from one in the Gross-Pitaevski
approach, is found. This form is valid beyond the Hartree-Fock approximation
and can be applied for arbitrary strong interparticle interaction.
