  The present article is concerned with the use of approximations in the
calculation of the many-body density of states (MBDS) of a system with total
energy E, composed by N bosons. In the mean-field framework, an integral
expression for MBDS, which is proper to be performed by asymptotic expansions,
can be derived. However, the standard second order steepest descent method
cannot be applied to this integral when the ground-state is sufficiently
populated. Alternatively, we derive a uniform formula for MBDS, which is
potentially able to deal with this regime. In the case of the one-dimensional
harmonic oscillator, using results found in the number theory literature, we
show that the uniform formula improves the standard expression achieved by
means of the second order method.
