The q-gamma and (q,q)-polygamma functions of Tsallis statistics

Robert K. Niven and Hiroki Suyari

Physica A: Statistical Mechanics and its Applications, 2009, vol. 388, issue 19, 4045-4060

Abstract: An axiomatic definition is given for the q-gamma function Γq(x),q∈R,q>0,x∈R of Tsallis (non-extensive) statistical physics, the continuous analogue of the q-factorial of Suyari [H. Suyari, Physica A 368 (1) (2006) 63], and the q-analogue of the gamma function Γ(x) of Euler and Gauss. A working definition in closed form, based on the Hurwitz and Riemann zeta functions (including their analytic continuations), is shown to satisfy this definition. Several relations involving the q-gamma and other functions are obtained. The (q,q)-polygamma functions ψq,q(m)(x),m∈N, defined by successive derivatives of lnqΓq(x), where lnqa=(1−q)−1(a1−q−1),a>0 is the q-logarithmic function, are also reported. The new functions are used to calculate the inferred probabilities and multipliers for Tsallis systems with finite numbers of particles N≪∞.

Keywords: Tsallis entropy; Non-extensive; q-algebra; Hurwitz zeta function; Combinatorial (search for similar items in EconPapers)
Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:388:y:2009:i:19:p:4045-4060

DOI: 10.1016/j.physa.2009.06.018

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