Asymptotic expansions of the gamma function related to Windschitl's formula

DOI10.1016/J.AMC.2014.07.080zbMath1335.41007OpenAlexW1991737430MaRDI QIDQ278595

Chao-Ping Chen

Publication date: 2 May 2016

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2014.07.080

zbMATH Keywords

gamma functionasymptotic expansionWindschitl's formula

Mathematics Subject Classification ID

Gamma, beta and polygamma functions (33B15) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60)

Related Items (17)

A more accurate approximation for the gamma function ⋮ An accurate approximation formula for gamma function ⋮ Windschitl type approximation formulas for the gamma function ⋮ Some new asymptotic approximations of the gamma function based on Nemes' formula, Ramanujan's formula and Burnside's formula ⋮ A family of Windschitl type approximations for gamma function ⋮ Some asymptotic expansions on hyperfactorial functions and generalized Glaisher-Kinkelin constants ⋮ Sharp inequalities and asymptotic expansions for the gamma function ⋮ Inequalities, asymptotic expansions and completely monotonic functions related to the gamma function ⋮ Inequalities and asymptotic expansions for the gamma function related to Mortici's formula ⋮ Asymptotic expansions of Gurland's ratio and sharp bounds for their remainders ⋮ Asymptotic expansions related to hyperfactorial function and Glaisher-Kinkelin constant ⋮ Monotonicity properties, inequalities and asymptotic expansions associated with the gamma function ⋮ Two asymptotic expansions for gamma function developed by Windschitl's formula ⋮ On the asymptotic expansions of the gamma function related to the Nemes, Gosper and Burnside formulas ⋮ Padé approximant related to asymptotics for the gamma function ⋮ Unified approaches to the approximations of the gamma function ⋮ Asymptotic expansions for the gamma function in terms of hyperbolic functions

Cites Work

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• A generated approximation related to Gosper's formula and Ramanujan's formula
• Sharp inequalities related to Gosper's formula
• A generated approximation related to Burnside's formula
• Asymptotic formulae associated with the Wallis power function and digamma function
• Very accurate estimates of the polygamma functions
• Sharp upper and lower bounds for the gamma function
• Ramanujan's Lost Notebook

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