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

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

2010-04-05

arxiv.org/abs/1004.0588v1

Physics

Mathematical Physics

14 pages

Scientific paper

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 (\phi(z,s,v) is exploited to deduce new identities.

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