Explicit expressions for some linear Euler-type sums containing harmonic and skew-harmonic numbers

DOI10.7153/jca-2022-20-07OpenAlexW4312541005MaRDI QIDQ5885732

Seán Mark Stewart

Publication date: 4 April 2023

Published in: Journal of Classical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.7153/jca-2022-20-07

zbMATH Keywords

polygamma functionharmonic numberclosed-formlogarithmic integralsEuler sumDirichlet beta functionskew-harmonic number

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Numerical summation of series (65B10)

Uses Software

• DLMF
• Equator

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A formula of S. Ramanujan
• Some identities involving the Riemann zeta function
• Explicit evaluation of some quadratic Euler-type sums containing double-index harmonic numbers
• Log-hyperbolic tangent integrals and Euler sums
• The polygamma function \(\psi^{(k)}(x)\) for \(x={1\over 4}\) and \(x={3\over 4}\)
• Extensions of Euler harmonic sums
• Special Techniques for Solving Integrals
• Euler Sums and Contour Integral Representations
• How to Integrate It
• An integral transform related to series involving alternating harmonic numbers
• A natural companion to Catalan's constant
• POWER SERIES WITH SKEW-HARMONIC NUMBERS, DILOGARITHMS, AND DOUBLE INTEGRALS
• Some evaluation of harmonic number sums
• A New Method of Evaluating ζ(2n)
• In the shadow of Euler's greatness: adventures in the rediscovery of an intriguing sum

This page was built for publication: Explicit expressions for some linear Euler-type sums containing harmonic and skew-harmonic numbers