On some properties of the gamma function

DOI10.1016/j.exmath.2007.10.001zbMath1200.33002OpenAlexW2007620044MaRDI QIDQ2427145

Necdet Batir

Publication date: 8 May 2008

Published in: Expositiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.exmath.2007.10.001

zbMATH Keywords

gamma functionRiemann zeta-functiondigamma functioncomplete monotonicitypolygamma functions

Mathematics Subject Classification ID

Gamma, beta and polygamma functions (33B15) Inequalities involving other types of functions (26D07)

Related Items (16)

Bounds for triple gamma functions and their ratios ⋮ A necessary and sufficient condition for sequences to be minimal completely monotonic ⋮ A certain class of completely monotonic sequences ⋮ Topics in Special Functions III ⋮ Some exact constants for the approximation of the quantity in the Wallis' formula ⋮ Two-sided inequality involving the \(q\)-gamma function ⋮ A completely monotonic function used in an inequality of Alzer ⋮ Complete monotonicity results for some functions involving the gamma and polygamma functions ⋮ Some inequalities and monotonicity properties associated with the gamma and psi functions ⋮ On the estimation of the shape parameter of the gamma distribution in second-order asymptotics ⋮ Inequalities for \(q\)-gamma function ratios ⋮ On some complete monotonicity of functions related to generalized \(k\)-gamma function ⋮ Some inequalities and monotonicity properties associated with the gamma and psi functions and the BarnesG-function ⋮ A note on complete monotonicity of the remainder in Stirling's formula ⋮ A remark on a class of double inequalities of Batir ⋮ Some properties of functions related to completely monotonic functions

Cites Work

• Some classes of completely monotonic functions. II
• Inequalities for the gamma and \(q\)-gamma functions
• Generalized gamma convolutions and related classes of distributions and densities
• A probabilistic interpretation of complete monotonicity
• A class of logarithmically completely monotonic functions and the best bounds in the first Kershaw's double inequality
• Monotonicity properties of the gamma function
• A new lower bound in the second Kershaw's double inequality
• Error Bounds for Asymptotic Expansions of the Ratio of Two Gamma Functions
• Some Extensions of W. Gautschi's Inequalities for the Gamma Function
• Completely monotonic functions involving the gamma and $q$-gamma functions
• The Gamma Function: An Eclectic Tour
• ON RAMANUJAN'S DOUBLE INEQUALITY FOR THE GAMMA FUNCTION
• The best bounds in Gautschi's inequality
• Some properties of the gamma and psi functions, with applications
• Inequalities for Zero-Balanced Hypergeometric Functions
• On some inequalities for the gamma and psi functions
• On the asymptotic representation of the Euler gamma function by Ramanujan
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