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

International Journal of Mathematics and Mathematical Sciences, Dec 2007

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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M. Aslam Chaudhry, Asghar Qadir. Operator Representation of Fermi-Dirac and Bose-Einstein Integral Functions with Applications, International Journal of Mathematics and Mathematical Sciences, 2007, DOI: 10.1155/2007/80515