  It is believed that the canonical gravitational partition function $Z$
associated to the classical Boltzmann-Gibbs (BG) distribution $\frac {e^{-\beta
H}} {{\cal Z}}$ cannot be constructed because the integral needed for building
up $Z$ includes an exponential and thus diverges at the origin.
  We show here that, by recourse to 1) the analytical extension treatment
obtained for the first time ever, by Gradshteyn and Rizhik, via an appropriate
formula for such case and 2) the dimensional regularization approach of Bollini
and Giambiagi's (DR), one can indeed obtain finite gravitational results
employing the BG distribution. The BG treatment is considerably more involved
than its Tsallis counterpart. The latter needs only dimensional regularization,
the former requires, in addition, analytical extension.
