Generalized distributions and properties of the particles obeying gentile distribution in harmonic trap

Particles that are trapped into two dimensions may have spin other than integer or half integer values. Therefore, these particles may obey statistical distributions other than Bose-Einstein or Fermi-Dirac distributions. In addition, distributions different than bosonic and fermionic distributions are utilized for describing the statistics of interacting particles independent of dimension. For this reason; Haldene-Wu, g-on and Gentile statistics that are proposed as statistical distributions in the literature are introduced in this study. Then, the thermodynamical properties of particles which obey Gentile statistics and are in a harmonic trap is investigated. These results are compared with the thermodynamical quantities of the particles which obey Haldane-Wu statistics and are in a harmonic trap [1]. In appendix, A new way to find the value of occupation number for Gentile statistics is proposed.