Reviving the quadratic series of Au-Yeung

DOI10.7153/jca-06-09zbMath1412.40026OpenAlexW2564141380MaRDI QIDQ4627773

Ovidiu Furdui, Cornel Ioan Vălean

Publication date: 5 March 2019

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

Full work available at URL: https://doi.org/10.7153/jca-06-09

zbMATH Keywords

Riemann zeta functionharmonic numbersAbel's summation formulalogarithmic integralsquadratic series

Mathematics Subject Classification ID

Convergence and divergence of series and sequences (40A05) Integral methods for summability (40C10)

Related Items (9)

Euler sums and Stirling sums ⋮ Explicit formulas of Euler sums via multiple zeta values ⋮ In the shadow of Euler's greatness: adventures in the rediscovery of an intriguing sum ⋮ A new proof for a classical quadratic harmonic series ⋮ New results containing quadratic harmonic numbers ⋮ Evaluation of a cubic Euler sum ⋮ A master theorem of series and an evaluation of a cubic harmonic series ⋮ Unnamed Item ⋮ Explicit evaluation of some quadratic Euler-type sums containing double-index harmonic numbers

Uses Software

• DLMF

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Explicit evaluation of Euler and related sums
• Limits, series, and fractional part integrals. Problems in mathematical analysis
• Series representations for some mathematical constants
• Series Involving Products of Two Harmonic Numbers
• Problems in Real Analysis
• On an Intriguing Integral and Some Series Related to ζ(4)

This page was built for publication: Reviving the quadratic series of Au-Yeung