The q-gamma and (q,q)-polygamma functions of Tsallis statistics |
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Authors: | Robert K Niven Hiroki Suyari |
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Institution: | a School of Aerospace, Civil and Mechanical Engineering, The University of New South Wales at ADFA, Northcott Drive, Canberra, ACT, 2600, Australia b Niels Bohr Institute, University of Copenhagen, Copenhagen Ø, Denmark c Department of Information and Image Sciences, Faculty of Engineering, Chiba University, 263-8522, Japan |
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Abstract: | An axiomatic definition is given for the q-gamma function 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 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 , defined by successive derivatives of , 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?∞. |
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Keywords: | 02 30 -f 02 30 Gp 02 50 Cw 05 90 +m |
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