Inequalities and asymptotic expansions associated with the Ramanujan and nemes formulas for the gamma function

DOI10.1016/j.amc.2015.04.010zbMath1410.33004OpenAlexW1995856835MaRDI QIDQ1643310

Chao-Ping Chen

Publication date: 19 June 2018

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

Full work available at URL: https://doi.org/10.1016/j.amc.2015.04.010

zbMATH Keywords

gamma functionasymptotic expansioninequality

Mathematics Subject Classification ID

Gamma, beta and polygamma functions (33B15) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Approximation by polynomials (41A10) Fourier coefficients, Fourier series of functions with special properties, special Fourier series (42A16) Inequalities involving other types of functions (26D07)

Related Items (10)

A more accurate approximation for the gamma function ⋮ Sharp inequalities and asymptotic expansions for 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 ⋮ Monotonicity properties, inequalities and asymptotic expansions associated with the gamma function ⋮ Inequalities and asymptotic expansions related to the volume of the unit ball in \(\mathbb{R}^n\) ⋮ On the asymptotic expansions of the gamma function related to the Nemes, Gosper and Burnside formulas ⋮ Padé approximant related to Ramanujan's formula for the gamma function ⋮ Padé approximant related to asymptotics for the gamma function ⋮ Asymptotic expansions for the gamma function in terms of hyperbolic functions

Cites Work

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• A refinement of Ramanujan's factorial approximation
• Ramanujan's estimate for the gamma function via monotonicity arguments
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• Remarks on some completely monotonic functions
• A new fast asymptotic series for the gamma function
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• Completely monotonic functions of positive order and asymptotic expansions of the logarithm of Barnes double gamma function and Euler's gamma function
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• A sharp version of Ramanujan's inequality for the factorial function
• Asymptotic formulae associated with the Wallis power function and digamma function
• ON RAMANUJAN'S DOUBLE INEQUALITY FOR THE GAMMA FUNCTION
• On some inequalities for the gamma and psi functions
• Ramanujan's Lost Notebook
• On the asymptotic representation of the Euler gamma function by Ramanujan
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