Rational series for multiple zeta and log gamma functions

DOI10.1016/j.jnt.2013.05.016zbMath1297.11107OpenAlexW2167441396MaRDI QIDQ740925

Paul Thomas Young

Publication date: 9 September 2014

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2013.05.016

zbMATH Keywords

Hurwitz zeta functionBernoulli polynomialsmultiple gamma functionsDirichlet \(L\)-functionspolygamma functionsmultiple zeta functionsBarnes zeta functions

Mathematics Subject Classification ID

Bernoulli and Euler numbers and polynomials (11B68) Hurwitz and Lerch zeta functions (11M35) Multiple Dirichlet series and zeta functions and multizeta values (11M32)

Related Items

A note on some constants related to the zeta-function and their relationship with the Gregory coefficients ⋮ Two series expansions for the logarithm of the gamma function involving Stirling numbers and containing only rational coefficients for certain arguments related to \(\pi^{-1}\) ⋮ Global series for height 1 multiple zeta functions ⋮ Absolute series for higher Euler constants ⋮ Three notes on Ser's and Hasse's representations for the zeta-functions ⋮ On shifted Mascheroni series and hyperharmonic numbers ⋮ Symmetries of Bernoulli polynomial series and Arakawa-Kaneko zeta functions ⋮ The \(p\)-adic Arakawa-Kaneko zeta functions and \(p\)-adic Lerch transcendent ⋮ Representations for the derivative at zero and finite parts of the Barnes zeta function

Cites Work

• Values of Dirichlet \(L\)-functions, Gauss sums and trigonometric sums
• Identities for the Riemann zeta function
• A hybrid of Darboux's method and singularity analysis in combinatorial asymptotics
• Sum of powers from uniform distribution moments
• Identities for the Hurwitz zeta function, gamma function, and \(L\)-functions
• The Cauchy numbers
• On Barnes' multiple zeta and gamma functions
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