Gentile statistics with a large maximum occupation number

In Gentile statistics the maximum occupation number can take on unrestricted integers: $1<n<\mathrm{\infty }$. 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 $$-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.