Evaluation of harmonic sums with integrals

DOI10.1090/qam/1499zbMath1397.40001arXiv1710.03637OpenAlexW2761796599MaRDI QIDQ4563565

Vivek Kaushik, Daniele Ritelli

Publication date: 1 June 2018

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

Full work available at URL: https://arxiv.org/abs/1710.03637

zbMATH Keywords

random variablespolytopemultiple integralsBasel problem

Mathematics Subject Classification ID

Probability distributions: general theory (60E05) Convergence and divergence of series and sequences (40A05) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60)

Related Items (1)

A Wilf–Zeilberger–Based Solution to the Basel Problem With Applications

Cites Work

• \(\zeta (n)\) via hyperbolic functions
• New definite integrals and a two-term dilogarithm identity
• A proof that Euler missed: Evaluating \(\zeta\) (2) the easy way
• Two poset polytopes
• Euler's formulae for \(\zeta(2n)\) and products of Cauchy variables
• Another Proof of <tex-math> ${\zeta(2)=\frac{\pi^2}{6}}$ </tex-math> Using Double Integrals
• Comment on the sums
• Probabilistically Proving that ζ(2) = π²⁄6
• EVALUATION OF CERTAIN ALTERNATING SERIES
• QUANTUM GRAVITATIONAL CORRECTIONS TO THE HYDROGEN ATOM AND HARMONIC OSCILLATOR
• Table errata: Table of integrals, series, and products [corrected and enlarged edition, Academic Press, New York, 1980; MR 81g:33001 by I. S. Gradshteyn [I. S. Gradshteĭn] and I. M. Ryzhik]
• Another Simple Proof of 1 + 1 2 2 + 1 3 2 + ⋅⋅⋅ = π 2 6
• On the Sums ∑ k = -∞ ∞ (4k + 1) -n
• Six Ways to Sum a Series
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