Integral and series representations of Riemann's zeta function and Dirichlet's eta function and a medley of related results

DOI10.1155/2013/181724zbMath1280.11047arXiv1208.3429OpenAlexW3105552015WikidataQ21285107 ScholiaQ21285107MaRDI QIDQ355654

Michael S. Milgram

Publication date: 25 July 2013

Published in: Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1208.3429

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Dedekind eta function, Dedekind sums (11F20)

Related Items (13)

Unnamed Item ⋮ Closed-form calculation of infinite products of Glaisher-type related to Dirichlet series ⋮ An integral equation for Riemann's zeta function and its approximate solution ⋮ Achronal averaged null energy condition for extremal horizons and (A)dS ⋮ Further exploration of Riemann's functional equation ⋮ Uncovering functional relationships at zeros with special reference to Riemann's Zeta Function ⋮ Zeta identities in parameter form ⋮ Evaluation of spherical GJMS determinants ⋮ On the concavity of Dirichlet's eta function and related functional inequalities ⋮ Trace Formulas Applied to the Riemann ζ-Function ⋮ On the Stieltjes constants and gamma functions with respect to alternating Hurwitz zeta functions ⋮ Unnamed Item ⋮ A series representation for Riemann's zeta function and some interesting identities that follow

Uses Software

• DLMF

Cites Work

• Symbolic and numeric computations of the Barnes function
• Uniform asymptotic approximations for incomplete Riemann zeta functions
• Multiple gamma and related functions
• Small perturbations of the Riemann zeta function and their zeros
• Evaluations of some classes of the trigonometric moment integrals
• The special functions and their approximations. Vol. I, II
• The Generalized Integro-Exponential Function
• Stirling's Series and Bernoulli Numbers
• Some series of the zeta and related functions
• Euler Sums and Contour Integral Representations
• Some theorems on perturbation theory
• Some definite integrals associated with the Riemann zeta function
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