  In Gentile statistics the maximum occupation number can take on unrestricted
integers: $1<n<\infty $. It is usually believed that Gentile statistics will
reduce to Bose-Einstein statistics when n equals the total number of particles
in the system N. In this paper, we will show that this statement is valid only
when the fugacity z<1; nevertheless, if z>1 the Bose-Einstein case is not
recovered from Gentile statistics as n goes to % N . Attention is also
concentrated on the contribution of the ground state which was ignored in
related literature. The thermodynamic behavior of a $% \nu $-dimensional
Gentile ideal gas of particle of dispersion $E=\frac{p^{s}%}{2m}$, where $\nu $
and s are arbitrary, is analyzed in detail. Moreover, we provide an alternative
derivation of the partition function for Gentile statistics.
