On an interpolating statistics from general principles

From an explicit construction of the many particle states, we demonstrate that q-basic numbers arise naturally in a theory which interpolates between Bose–Einstein and Fermi–Dirac statistics. We formulate such a theory based on the principle of detailed balance. We obtain a transcendental equation for the distribution function and seek a series solution. This theory has the correct Boson limit but the Fermion limit leads to generalized Fermions not obeying the exclusion principle. We also express the distribution function as an infinite continued fraction. The first approximant of the theory reproduces the distribution function of our earlier work. Some general results from the exact theory are summarized.