Sharp approximation formulas and inequalities for the Wallis ratio by continued fraction

DOI10.1016/j.jmaa.2017.06.063zbMath1406.11123OpenAlexW2727758122MaRDI QIDQ2014127

Xu You, Di-Rong Chen

Publication date: 10 August 2017

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.2017.06.063

zbMATH Keywords

gamma functioninequalitiesWallis ratiomultiple-correction method

Mathematics Subject Classification ID

Gamma, beta and polygamma functions (33B15) Continued fractions (11A55) Evaluation of number-theoretic constants (11Y60)

Cites Work

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• Some best approximation formulas and inequalities for the Wallis ratio
• Some exact constants for the approximation of the quantity in the Wallis' formula
• Integral representations and complete monotonicity related to the remainder of Burnside's formula for the gamma function
• Multiple-correction and continued fraction approximation
• New improvements of the Stirling formula
• Multiple-correction and continued fraction approximation. II
• A continued fraction approximation of the gamma function
• Multiple-correction and faster approximation
• Product Approximations via Asymptotic Integration
• Some inequalities constructed by Tchebysheff's integral inequality
• The best bounds in Wallis’ inequality

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