  The non extensive thermodynamics of an ideal gas composed by bosons and/or
fermions is derived from its partition function for systems with finite
chemical potentials. It is shown that the thermodynamical quantities derived in
the present work are in agreement with those obtained in previous works when
$\mu \le m$. However some inconsistencies of previous references are corrected
when $\mu > m$. A discontinuity in the first derivatives of the partition
function and its effects are discussed in detail. We show that at similar
conditions, the non extensive statistics provide a harder equation of state
than that provided by the Boltzmann-Gibbs statistics.
