International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 2007 / Article

Research Article | Open Access

Volume 2007 |Article ID 080515 | https://doi.org/10.1155/2007/80515

M. Aslam Chaudhry, Asghar Qadir, "Operator Representation of Fermi-Dirac and Bose-Einstein Integral Functions with Applications", International Journal of Mathematics and Mathematical Sciences, vol. 2007, Article ID 080515, 9 pages, 2007. https://doi.org/10.1155/2007/80515

Operator Representation of Fermi-Dirac and Bose-Einstein Integral Functions with Applications

Academic Editor: Virginia Kiryakova
Received03 Apr 2007
Accepted02 Sep 2007
Published30 Dec 2007

Abstract

Fermi-Dirac and Bose-Einstein functions arise as quantum statistical distributions. The Riemann zeta function and its extension, the polylogarithm function, arise in the theory of numbers. Though it might not have been expected, these two sets of functions belong to a wider class of functions whose members have operator representations. In particular, we show that the Fermi-Dirac and Bose-Einstein integral functions are expressible as operator representations in terms of themselves. Simpler derivations of previously known results of these functions are obtained by their operator representations.

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Copyright © 2007 M. Aslam Chaudhry and Asghar Qadir. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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