Refinements of Gurland's formula for pi

DOI10.1016/j.camwa.2011.07.073zbMath1231.33002OpenAlexW2068118651MaRDI QIDQ660927

Cristinel Mortici

Publication date: 5 February 2012

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2011.07.073

zbMATH Keywords

gamma functiondigamma functioncompletely monotonic functionsWallis ratiopolygamma functionsratio of gamma functions

Mathematics Subject Classification ID

Gamma, beta and polygamma functions (33B15) Exponential and trigonometric functions (33B10)

Related Items (10)

Wallis' sequence estimated accurately using an alternating series ⋮ Further refinements of Gurland's formula for \({\pi}\) ⋮ Sharp inequalities related to the volume of the unit ball in \(\mathbb{R}^n\) ⋮ Birth, growth and computation of pi to ten trillion digits ⋮ Inequalities, asymptotic expansions and completely monotonic functions related to the gamma function ⋮ A simple asymptotic estimate of Wallis' ratio using Stirling's factorial formula ⋮ Basic asymptotic estimates for powers of Wallis’ ratios ⋮ An inequality for the gamma function via statistics and applications ⋮ Simple accurate balanced asymptotic approximation of Wallis' ratio using Euler-Boole alternating summation ⋮ Padé approximant related to the Wallis formula

Cites Work

• Unnamed Item
• A class of integral approximations for the factorial function
• On new sequences converging towards the Euler-Mascheroni constant
• New approximations of the gamma function in terms of the digamma function
• Monotonicity properties of the volume of the unit ball in \({\mathbb{R}^{n}}\)
• Sharp inequalities related to Gosper's formula
• On Wallis' Formula
• Very accurate estimates of the polygamma functions
• What is the Laplace Transform?

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