Some exact constants for the approximation of the quantity in the Wallis' formula

DOI10.1186/1029-242X-2013-67zbMath1281.41010WikidataQ59301877 ScholiaQ59301877MaRDI QIDQ395781

Jian-Guo Xu, Feng Qi, Sen-Lin Guo

Publication date: 30 January 2014

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

zbMATH Keywords

gamma functionapproximationStirling's formulaWallis' formula

Mathematics Subject Classification ID

Gamma, beta and polygamma functions (33B15) Other analytical inequalities (26D20) Best constants in approximation theory (41A44)

Related Items

Some inequalities for the ratio of gamma functions, Some best approximation formulas and inequalities for the Wallis ratio, A certain class of completely monotonic sequences, Some quicker approximations and inequalities of the Wallis ratio by continued fraction, Some properties of central Delannoy numbers, Improved approximation formulas and inequalities for the Wallis ratio, The perimeter of a flattened ellipse can be estimated accurately even from Maclaurin’s series, Logarithmically completely monotonic functions and applications, Simple, accurate, asymptotic estimates for the ratio of two gamma functions, Bounds for the ratio of two gamma functions: from Wendel's asymptotic relation to Elezović-Giordano-Pečarić's theorem, Sharp approximation formulas and inequalities for the Wallis ratio by continued fraction, A simple asymptotic estimate of Wallis' ratio using Stirling's factorial formula, How is the period of a simple pendulum growing with increasing amplitude?, Taylor's series expansions for real powers of two functions containing squares of inverse cosine function, closed-form formula for specific partial Bell polynomials, and series representations for real powers of pi, Some properties of functions related to completely monotonic functions, Basic asymptotic estimates for powers of Wallis’ ratios, Simple accurate balanced asymptotic approximation of Wallis' ratio using Euler-Boole alternating summation

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