A new method for derivation of statistical weight of the Gentile Statistics

• We obtain statistical weight of Gentile distribution (GD) using inductive method.
• We calculate the statistical weight for various intermediate particles obeying GD.
• The inductive method needs less computer time compared to previous methods.

We present a new method for obtaining the statistical weight of the Gentile Statistics. In a recent paper, Perez and Tun presented an approximate combinatoric and an exact recursive formula for the statistical weight of Gentile Statistics, beginning from bosonic and fermionic cases, respectively Hernandez-Perez and Tun (2007). In this paper, we obtain two exact, one combinatoric and one recursive, formulae for the statistical weight of Gentile Statistics, by another approach. The combinatoric formula is valid only for special cases, whereas recursive formula is valid for all possible cases. Moreover, for a given q-maximum number of particles that can occupy a level for Gentile statistics-the recursive formula we have derived gives the result much faster than the recursive formula presented in Hernandez-Perez and Tun (2007), when one uses a computer program. Moreover we obtained the statistical weight for the distribution proposed by Dai and Xie (2009).