Some new convergent sequences of Glaisher-Kinkelin's and Bendersky-Adamchik's constants

DOI10.1007/s00025-015-0497-4zbMath1400.11167OpenAlexW2267030766MaRDI QIDQ511818

Songhao Liu, Dawei Lu

Publication date: 22 February 2017

Published in: Results in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00025-015-0497-4

zbMATH Keywords

rate of convergenceasymptotic expansioninequalityBendersky-Adamchik's constantsGlaisher-Kinkelin's constant

Mathematics Subject Classification ID

Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Inequalities for sums, series and integrals (26D15) Continued fractions (11A55) Evaluation of number-theoretic constants (11Y60)

Cites Work

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• A new Stirling series as continued fraction
• On new sequences converging towards the Euler-Mascheroni constant
• Certain classes of series involving the zeta function
• Certain classes of series associated with the zeta function and multiple gamma functions
• A continued fraction approximation of the gamma function
• Approximating the constants of Glaisher-Kinkelin type
• A new quicker sequence convergent to Euler's constant
• Product Approximations via Asymptotic Integration
• A Quicker Convergence to Euler's Constant
• Very accurate estimates of the polygamma functions

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