This article is cited in 5 papers

,Fermi–Dirac and Bose–Einstein functions of negative integer order

D. Cvijović

Atomic Physics Laboratory, Vinča Institute of Nuclear Sciences, Belgrade, Republic of Serbia

Abstract: 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.

Received: 30.04.2009

DOI: 10.4213/tmf6449

 English version: Theoretical and Mathematical Physics, 2009, 161:3, 1663–1668

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