A generated approximation of the gamma function related to Windschitl's formula

DOI10.1016/J.JNT.2014.01.023zbMath1296.33005OpenAlexW2058704243MaRDI QIDQ401987

Congxu Ma, Dawei Lu, Lixin Song

Publication date: 27 August 2014

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2014.01.023

zbMATH Keywords

gamma functioninequalitiesrate of convergencecontinued fractionsStirling's formulaWindschitl's formulafactorial function

Mathematics Subject Classification ID

Gamma, beta and polygamma functions (33B15) Approximation by polynomials (41A10) Rate of convergence, degree of approximation (41A25)

Related Items (19)

A more accurate approximation for the gamma function ⋮ An accurate approximation formula for gamma function ⋮ Windschitl type approximation formulas for the gamma function ⋮ Asymptotic expansions of the gamma function related to Windschitl's formula ⋮ 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 new approximations and inequalities of the sequence \((1+1/n)^n\) and improvements of Carleman's inequality ⋮ Asymptotic expansions for the psi function and the Euler-Mascheroni constant ⋮ Sharp inequalities and asymptotic expansions for the gamma function ⋮ Inequalities, asymptotic expansions and completely monotonic functions related to the gamma function ⋮ 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 ⋮ A new approximation of the gamma function by expanding the Windschitl's formula ⋮ Padé approximant related to asymptotics for the gamma function ⋮ Inequalities and asymptotic expansions for the gamma function ⋮ On some convergence to the constant \(e\) and proof of Keller's limit ⋮ Asymptotic expansions for the gamma function ⋮ Asymptotic expansions for the gamma function in terms of hyperbolic functions

Cites Work

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• Ramanujan formula for the generalized Stirling approximation
• A new Stirling series as continued fraction
• New improvements of the Stirling formula
• On new sequences converging towards the Euler-Mascheroni constant
• New asymptotic expansion for the gamma function
• A continued fraction approximation of the gamma function
• Product Approximations via Asymptotic Integration
• Very accurate estimates of the polygamma functions
• On some inequalities for the gamma and psi functions

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