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Fourier Transform Representation of the Extended Fermi-Dirac and Bose-Einstein Functions with Applications to the Family of the Zeta and Related Functions

2011/04/21 by Asifa Tassaddiq, Asghar Qadir, Tassaddiq, Asifa +1
Mathematics · Physics and Astronomy · #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications #Advanced Thermodynamics and Statistical Mechanics #Analytic Number Theory Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Mechanics and Applications #math-ph #math.CA #math.MP

paper · pdf · doi:10.48550/arxiv.1104.4346

13 pages only

arxiv created 2011/04/21 · openalex publication_date 2011/04/21 · arxiv updated 2011/04/25 · openalex created_date 2025/10/27 · openalex updated_date 2026/07/28

Abstract

On the one hand the Fermi-Dirac and Bose-Einstein functions have been extended in such a way that they are closely related to the Riemann and other zeta functions. On the other hand the Fourier transform representation of the gamma and generalized gamma functions proved useful in deriving various integral formulae for these functions. In this paper we use the Fourier transform representation of the extended functions to evaluate integrals of products of these functions. In particular we evaluate some integrals containing the Riemann and Hurwitz zeta functions, which had not been evaluated before.

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