Further refinements of Gurland's formula for \({\pi}\)

DOI10.1186/1029-242X-2013-48zbMath1282.33004WikidataQ59294205 ScholiaQ59294205MaRDI QIDQ395811

Long Lin

Publication date: 30 January 2014

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

zbMATH Keywords

gamma functioninequalityasymptotic formulapsi functionWallis ratio

Mathematics Subject Classification ID

Gamma, beta and polygamma functions (33B15) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Inequalities involving other types of functions (26D07)

Related Items (9)

Some best approximation formulas and inequalities for the Wallis ratio ⋮ Inequalities and asymptotic expansions associated with the Wallis sequence ⋮ Sharp inequalities and asymptotic expansion associated with the Wallis sequence ⋮ Sharp inequalities related to the volume of the unit ball in \(\mathbb{R}^n\) ⋮ Birth, growth and computation of pi to ten trillion digits ⋮ 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 ⋮ Padé approximant related to the Wallis formula

Cites Work

• Completely monotone functions and the Wallis ratio
• New approximation formulas for evaluating the ratio of gamma functions
• Refinements of Gurland's formula for pi
• New approximations of the gamma function in terms of the digamma function
• Completely monotonic and related functions
• Product Approximations via Asymptotic Integration
• On Wallis' Formula
• The best bounds in Wallis’ inequality

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