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. 
@article{TMF_2009_161_3_a7,
     author = {D. Cvijovi\'c},
     title = {,Fermi--Dirac and {Bose--Einstein} functions of negative integer order},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {400--405},
     publisher = {mathdoc},
     volume = {161},
     number = {3},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2009_161_3_a7/}
}
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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/