Gentile statistics with a large maximum occupation number

In Gentile statistics the maximum occupation number can take on unrestricted integers: 11 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 ν-dimensional Gentile ideal gas of particle of dispersion E=ps/2m, where ν and s are arbitrary, is analyzed in detail. Moreover, we provide an alternative derivation of the partition function for Gentile statistics