Some new approximations of Glaisher-Kinkelin's and Bendersky-Adamchik's constants by continued fraction

DOI10.1016/J.JNT.2015.12.008zbMath1408.11118OpenAlexW2296731133MaRDI QIDQ5964548

Cristinel Mortici, Lixin Song, Dawei Lu

Publication date: 29 February 2016

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2015.12.008

zbMATH Keywords

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

Mathematics Subject Classification ID

Continued fractions (11A55) Rate of convergence, degree of approximation (41A25) 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 set of mathematical constants arising naturally in the theory of the 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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