An asymptotic approximation of Wallis' sequence

DOI10.2478/s11533-011-0138-4zbMath1252.40002OpenAlexW2068909993MaRDI QIDQ424091

Vito Lampret

Publication date: 31 May 2012

Published in: Central European Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2478/s11533-011-0138-4

zbMATH Keywords

rate of convergenceapproximationestimateWallis' ratio

Mathematics Subject Classification ID

Approximation to limiting values (summation of series, etc.) (40A25) Evaluation of number-theoretic constants (11Y60)

Related Items (11)

Some inequalities for the ratio of gamma functions ⋮ Inequalities and completely monotonic functions associated with the ratios of functions resulting from the gamma function ⋮ Wallis' sequence estimated accurately using an alternating series ⋮ Inequalities and asymptotic expansions associated with the Wallis sequence ⋮ Sharp inequalities and asymptotic expansion associated with the Wallis sequence ⋮ Series representations of the remainders in the expansions for certain functions with applications ⋮ Sharp inequalities related to the volume of the unit ball in \(\mathbb{R}^n\) ⋮ Asymptotic expansions for the Wallis sequence and some new mathematical constants associated with the Glaisher-Kinkelin and Choi-Srivastava constants ⋮ Inequalities, asymptotic expansions and completely monotonic functions related to the gamma function ⋮ On the asymptotic expansions of products related to the Wallis, Weierstrass, and Wilf formulas ⋮ Basic asymptotic estimates for powers of Wallis’ ratios

Uses Software

• Mathematica

Cites Work

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• New approximation formulas for evaluating the ratio of gamma functions
• Sharp inequalities and complete monotonicity for the Wallis ratio
• Alternative proof of the best bounds of Wallis' inequality
• A new method for establishing and proving accurate bounds for the Wallis ratio
• On Wallis' formula
• A Modified Wallis Product and Some Applications
• Ramanujan, Modular Equations, and Approximations to Pi or How to Compute One Billion Digits of Pi
• The best bounds in Wallis’ inequality

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