Lee, in a series of papers, described a unified formulation of the statistical thermodynamics of ideal quantum gases in terms of the polylogarithm functions. Li(s)(z). It is aimed here to investigate the functions Li(s)(z), for s = 0, -1, -2, which are, following Lee. referred to as the polypseudologarithms (or polypseudologs) of order n equivalent to -s Various known results regarding polypseudologs, mainly obtained in widely differing contexts and currently scattered throughout the literature, have been brought together along with many new results and insights and they all have been proved in a simple and unified manner. In addition, a new general explicit closed-form formula for these functions involving the Carlitz-Scoville higher tangent numbers has been established (C) 2009 Elsevier B.V. All rights reserved.
Keywords:Polylogarithms / Polypseudologarithms / Stirling numbers of second kind / Eulerian numbers / Higher tangent numbers
Source:Physica A: Statistical Mechanics and Its Applications, 2010, 389, 8, 1594-1600
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