Concerning an infinite series of Ramanujan related to the natural logarithm

DOI10.1007/s11139-017-9961-yOpenAlexW2775281639MaRDI QIDQ1623878

David M. Bradley

Publication date: 15 November 2018

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11139-017-9961-y

zbMATH Keywords

Bernoulli numberscompletely monotone functionEuler's constantnatural logarithm

Mathematics Subject Classification ID

Bernoulli and Euler numbers and polynomials (11B68) Computation of special functions and constants, construction of tables (65D20) Inequalities for sums, series and integrals (26D15) Monotonic functions, generalizations (26A48) Evaluation of number-theoretic constants (11Y60)

Uses Software

• DLMF

Cites Work

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• Euler's constant, \(q\)-logarithms, and formulas of Ramanujan and Gosper
• A probabilistic interpretation of complete monotonicity
• Completely monotonic rational functions and Hall's marriage theorem
• Computational strategies for the Riemann zeta function
• Euler’s constant: Euler’s work and modern developments
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• Error Bounds for Asymptotic Expansions of the Ratio of Two Gamma Functions
• The Arithmetic-Geometric Mean and Fast Computation of Elementary Functions
• A Note on Completely and Absolutely Monotone Functions
• Higher Monotonicity Properties of Certain Sturm-Liouville Functions. III
• Explicit Formulas for Bernoulli Numbers
• Bernstein functions. Theory and applications

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