International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 80515, 9 pages
doi:10.1155/2007/80515
Research Article
Operator Representation of Fermi-Dirac and Bose-Einstein Integral Functions with Applications
1Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
2Centre for Advanced Mathematics and Physics, National University of Sciences and Technology, Campus of the College of Electrical and Mechanical Engineering, Peshawar Road, Rawalpindi, Pakistan
Received 3 April 2007; Accepted 2 September 2007
Academic Editor: Virginia Kiryakova
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.
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.