Haldane–Wu statistics and Rogers dilogarithm

The Haldane–Wu exclusion statistics is considered from the generalized extensive statistics point of view and certain related mathematical aspects are investigated. A series representation for the corresponding generating function is proven. Equivalence of two formulas for the central charge, derived for the Haldane–Wu statistics via the thermodynamic Bethe ansatz, is established. As a corollary, a series representation with a free parameter for the Rogers dilogarithm is found. It is shown that the generating function, the entropy, and the central charge for the Gentile statistics majorize those for the Haldane–Wu statistics (under appropriate choice of parameters). From this, some dilogarithm inequality is derived.