  We theoretically examine equilibrium properties of the harmonically trapped
ideal Bose and Fermi gases in the quantum degeneracy regime. We analyze
thermodynamic characteristics of gases with a finite number of atoms by means
of the known semiclassical approach and perform comparison with exact numerical
results. For a Fermi gas, we demonstrate deviations in the Fermi energy values
originating from a discrete level structure and show that these are observable
only for a small number of particles. For a Bose gas, we observe characteristic
softening of phase transition features, which contrasts to the semiclassical
predictions and related approximations. We provide a more accurate methodology
of determining corrections to the critical temperature due to finite number of
particles.
