Some New Results Involving the Generalized Bose-Einstein and Fermi-Dirac Functions
Date
2019
Authors
Srivastava, Rekha
Naaz, Humera
Kazi, Sabeena
Tassaddiq, Asifa
Journal Title
Journal ISSN
Volume Title
Publisher
Axioms
Abstract
In this paper, we obtain a new series representation for the generalized Bose–Einstein and Fermi–Dirac functions by using fractional Weyl transform. To achieve this purpose, we obtain an analytic continuation for these functions by generalizing the domain of Riemann zeta functions from (0<R(s)<1) to (0<R(s)<μ). This leads to fresh insights for a new generalization of the Riemann zeta function. The results are validated by obtaining the classical series representation of the polylogarithm and Hurwitz–Lerch zeta functions as special cases. Fractional derivatives and the relationship of the generalized Bose–Einstein and Fermi–Dirac functions with Apostol–Euler–Nörlund polynomials are established to prove new identities.
Description
Keywords
Fermi-Dirac function, Bose-Einstein function, Weyl transform, series representation
Citation
Srivastava, R., Naaz, H., Kazi, S., & Tassaddiq, A. (2019). Some New Results Involving the Generalized Bose-Einstein and Fermi-Dirac Functions. Axioms. 8(2), 1-12. https://doi.org/10.3390/axioms8020063.