Completely monotone functions and the Wallis ratio

DOI10.1016/j.aml.2011.10.008zbMath1242.33005OpenAlexW1984752375MaRDI QIDQ429190

Cristinel Mortici

Publication date: 26 June 2012

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2011.10.008

zbMATH Keywords

gamma functioncompletely monotonic functionsWallis ratiopolygamma functionsratio of gamma functionsKazarinoff's inequality

Mathematics Subject Classification ID

Gamma, beta and polygamma functions (33B15) Inequalities for sums, series and integrals (26D15)

Related Items (14)

Estimates for Wallis' ratio and related functions ⋮ Inequalities and asymptotic expansions associated with the Wallis sequence ⋮ Sharp inequalities and asymptotic expansion associated with the Wallis sequence ⋮ Further refinements of Gurland's formula for \({\pi}\) ⋮ Asymptotic expansions for the Wallis sequence and some new mathematical constants associated with the Glaisher-Kinkelin and Choi-Srivastava constants ⋮ The perimeter of a flattened ellipse can be estimated accurately even from Maclaurin’s series ⋮ On the asymptotic expansions of products related to the Wallis, Weierstrass, and Wilf formulas ⋮ Some conditions for a class of functions to be completely monotonic ⋮ A sharp two-sided inequality for bounding the Wallis ratio ⋮ A simple asymptotic estimate of Wallis' ratio using Stirling's factorial formula ⋮ Robust Geodesic Regression ⋮ How is the period of a simple pendulum growing with increasing amplitude? ⋮ Basic asymptotic estimates for powers of Wallis’ ratios ⋮ Simple accurate balanced asymptotic approximation of Wallis' ratio using Euler-Boole alternating summation

Cites Work

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• Ramanujan formula for the generalized Stirling approximation
• On Wallis' formula
• What is the Laplace Transform?

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