A natural companion to Catalan's constant

DOI10.7153/jca-2021-18-09zbMath1499.33016OpenAlexW3208878043MaRDI QIDQ5078340

Amrik Singh Nimbran, Paul Levrie, John Maxwell Campbell

Publication date: 23 May 2022

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

Full work available at URL: https://doi.org/10.7153/jca-2021-18-09

zbMATH Keywords

trilogarithmsymbolic evaluationCatalan's constantEuler-type sum

Mathematics Subject Classification ID

Gamma, beta and polygamma functions (33B15) Generalized hypergeometric series, ({}_pF_q) (33C20) Higher logarithm functions (33B30)

Related Items (6)

Explicit expressions for some linear Euler-type sums containing harmonic and skew-harmonic numbers ⋮ Variant Alternating Euler Sums of Higher Order ⋮ Explicit identities for infinite families of series involving squared binomial coefficients ⋮ A Wilf–Zeilberger–Based Solution to the Basel Problem With Applications ⋮ On a problem involving the squares of odd harmonic numbers ⋮ Logarithmic integrals with applications to BBP and Euler-type sums

Uses Software

• OEIS

Cites Work

• Alternative evaluation of a ln tan integral arising in quantum field theory
• On Stirling numbers and Euler sums
• Further Ramanujan-like series containing harmonic numbers and squared binomial coefficients
• A certain series associated with Catalan's constant
• On the interplay between hypergeometric series, Fourier-Legendre expansions and Euler sums
• New series involving harmonic numbers and squared central binomial coefficients
• On the interplay among hypergeometric functions, complete elliptic integrals, and Fourier-Legendre expansions
• Series containing squared central binomial coefficients and alternating harmonic numbers
• Identities for Catalan's constant arising from integrals depending on a parameter
• The Newest Inductee in the Number Hall of Fame
• Euler-like sums via powers of log, arctan and arctanh functions
• Some Identities Involving Harmonic Numbers
• Evaluation of a ln tan integral arising in quantum field theory
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