  The low-density expansions for the energy, chemical potential, and condensate
depletion of the homogeneous dilute dipolar Bose gas are obtained by
regularizing the dipole-dipole interaction at long distances. It is shown that
the leading term, proportional to the density, allows a simple physical
interpretation and consistently describes the thermodynamic stability of the
system. The long-range asymptotics are obtained analytically for the normal and
anomalous one-particle correlation functions and the pair distribution
function. We discuss the properties of the two-body scattering with zero
relative momentum for the dipole-dipole interaction, in particular, we derive
the asymptotics of the wave function and a correction to the scattering length
for small values of the dipolar range. We show how the density expansions can
be derived within the Bogoliubov model of weakly interacting particles without
any divergence from the assumption of universality of the expansions at low
densities.
