Improved continued fraction sequence convergent to the Somos' quadratic recurrence constant

DOI10.1016/J.JMAA.2015.12.013zbMath1378.11109OpenAlexW2295823469MaRDI QIDQ905979

Xu You, Di-Rong Chen

Publication date: 28 January 2016

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2015.12.013

zbMATH Keywords

continued fractiongeneralized Euler constantmultiple-correction methodSomos' quadratic recurrence constant

Mathematics Subject Classification ID

Inequalities for sums, series and integrals (26D15) Continued fractions (11A55) Rate of convergence, degree of approximation (41A25) Continued fraction calculations (number-theoretic aspects) (11Y65) Evaluation of number-theoretic constants (11Y60)

Related Items (11)

Some new continued fraction sequence convergent to the Somos quadratic recurrence constant ⋮ Inequalities and asymptotic expansions related to the generalized Somos quadratic recurrence constant ⋮ Approximation formulas related to Somos' quadratic recurrence constant ⋮ Some new sequences that converge to the Ioachimescu constant ⋮ Continued fraction inequalities related to \((1+\frac{1}{x})^x\) ⋮ Sharp inequalities and asymptotic series related to Somos' quadratic recurrence constant ⋮ Some approximations of Glaisher-Kinkelin and Bendersky-Adamchik constants ⋮ On new sequences converging towards the Ioachimescu's constant ⋮ Some sequences converging towards Ioachimescu's constant related to Ramanujan's formula ⋮ Asymptotic expansion related to the generalized Somos recurrence constant ⋮ Approximations of the generalized-Euler-constant function and the generalized Somos' quadratic recurrence constant

Uses Software

• OEIS

Cites Work

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• Multiple-correction and continued fraction approximation
• Estimating the Somos' quadratic recurrence constant
• The generalized-Euler-constant function \(\gamma (z)\) and a generalization of Somos's quadratic recurrence constant
• Double integrals and infinite products for some classical constants via analytic continuations of Lerch's transcendent
• Some new quicker convergences to Glaisher-Kinkelin's and Bendersky-Adamchik's constants
• Multiple-correction and faster approximation
• Some new continued fraction estimates of the Somos' quadratic recurrence constant
• Arithmetical properties of some series with logarithmic coefficients

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