Geodesic
,Fermi–Dirac and Bose–Einstein functions of negative integer order
Teoretičeskaâ i matematičeskaâ fizika, Tome 161 (2009) no. 3, pp. 400-405
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We find simple explicit closed-form formulas for the Fermi–Dirac function $\mathscr{F}_{-n}(z)$ and Bose–Einstein function $\mathscr{B}_{-n}(z)$ for arbitrary $n\in\mathbb{N}$. The obtained formulas involve the higher tangent numbers defined by Carlitz and Scoville. We present some examples and direct consequences of applying the main results.
Keywords: Fermi–Dirac function, Bose–Einstein function, Fermi–Dirac integral, Bose–Einstein integral, higher-order tangent number, order-$k$ tangent number. 
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D. Cvijović. ,Fermi–Dirac and Bose–Einstein functions of negative integer order. Teoretičeskaâ i matematičeskaâ fizika, Tome 161 (2009) no. 3, pp. 400-405. http://geodesic.mathdoc.fr/item/TMF_2009_161_3_a7/

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