Some New Results Involving the Generalized Bose–Einstein and Fermi–Dirac Functions

Axioms

Sabeena Kazi¹  Asifa Tassaddiq¹  Humera Naaz¹  Rekha Srivastava² 

[1] College of Computer and Information Sciences, Majmaah University, Al Majmaah 11952, Saudiarabia;Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada;

关键词: Fermi–Dirac function;    Bose–Einstein function;    Weyl transform;    series representation;   

DOI  :  10.3390/axioms8020063

来源: DOAJ

【 摘 要 】

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 $(0<\Re \left(\mathrm{s}\right)<1)$ to $\left(0<\Re \left(\mathrm{s}\right)<\mathsf{\mu }\right).$ 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.

【 授权许可】

Unknown