Abstract
The familiar Fermi-Dirac and Bose-Einstein functions are of importance not only for their role in quantum statistics, but also for their several interesting mathematical properties in themselves. Here, in our present investigation, we have extended these functions by introducing an extra parameter in a way that gives new insights into these functions and their relationship to the family of zeta functions. These extensions are dual to each other in a sense that is explained in this paper. Some identities are proved here for each of these general functions and their relationship with the general Hurwitz-Lerch zeta function Φ(z, s, a) is exploited to derive some other (presumably new) identities.
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