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

Autor:	Rekha Srivastava, Humera Naaz, Sabeena Kazi, Asifa Tassaddiq
Jazyk:	angličtina
Rok vydání:	2019
Předmět:	Fermi–Dirac function Bose–Einstein function Weyl transform series representation Mathematics QA1-939
Zdroj:	Axioms, Vol 8, Iss 2, p 63 (2019)
Druh dokumentu:	article
ISSN:	2075-1680
DOI:	10.3390/axioms8020063
Popis:	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.
Databáze:	Directory of Open Access Journals
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