Extended Fermi-Dirac and Bose-Einstein functions with applications to the family of zeta functions

2010/04/05 by M. A. Chaudhry, Chaudhry, M. Aslam, Asghar Qadir +4
Computer Science · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Quantum Information and Cryptography #Quantum Mechanics and Applications #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.1004.0588

14 pages

arxiv created 2010/04/05 · arxiv updated 2010/04/06

Abstract

Fermi-Dirac and Bose-Einstein integral functions are of importance not only in quantum statistics but for their mathematical properties, in themselves. Here, we have extended these functions by introducing an extra parameter in a way that gives new insights into these functions and their relation to the family of zeta functions. These extensions are "dual" to each other in a sense that is explained. Some identities are proved for them and the relation between them and the general Hurwitz-Lerch zeta function (ϕ(z,s,v) is exploited to deduce new identities.

Citations

• Riemann Zeta Function

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