A class of logarithmically completely monotonic functions and application to the best bounds in the second Gautschi-Kershaw's inequality

DOI10.1016/j.cam.2008.05.030zbMath1160.33001OpenAlexW1983461830MaRDI QIDQ1002192

Feng Qi

Publication date: 25 February 2009

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

Full work available at URL: https://doi.org/10.1016/j.cam.2008.05.030

zbMATH Keywords

gamma functiondi-gamma functionGautschi-Kershaw's inequalityWalli's ratio

Mathematics Subject Classification ID

Gamma, beta and polygamma functions (33B15) Numerical methods for integral transforms (65R10) Convexity of real functions in one variable, generalizations (26A51) Monotonic functions, generalizations (26A48) Other analytical inequalities (26D20)

Related Items (15)

Complete monotonicity of divided differences of the di- and tri-gamma functions with applications ⋮ Monotonicity of a mean related to polygamma functions with an application ⋮ Complete monotonicity involving some ratios of gamma functions ⋮ Some exact constants for the approximation of the quantity in the Wallis' formula ⋮ Some properties of the generalized Gaussian ratio and their applications ⋮ Some inequalities and monotonicity properties associated with the gamma and psi functions ⋮ A comparison theorem for two divided differences and applications to special functions ⋮ Some properties of the divided difference of psi and polygamma functions ⋮ Bounds for the ratio of two gamma functions ⋮ A class of completely mixed monotonic functions involving the gamma function with applications ⋮ A new asymptotic expansion of a ratio of two gamma functions and complete monotonicity for its remainder ⋮ Complete monotonicity and inequalites involving Gurland's ratios of gamma functions ⋮ Logarithmically complete monotonicity of ratios of \(q\)-gamma functions ⋮ On the Hadamard's inequality for log-convex functions on the coordinates ⋮ Complete monotonicity of the remainder of the asymptotic series for the ratio of two gamma functions

Uses Software

• Mathematica

Cites Work

• A complete monotonicity property of the gamma function
• A class of logarithmically completely monotonic functions and the best bounds in the first Kershaw's double inequality
• Integral representation of some functions related to the gamma function
• Some Elementary Inequalities Relating to the Gamma and Incomplete Gamma Function
• The gamma function inequalities of Gurland and Gautschi
• Some Extensions of W. Gautschi's Inequalities for the Gamma Function
• FOUR LOGARITHMICALLY COMPLETELY MONOTONIC FUNCTIONS INVOLVING GAMMA FUNCTION
• On Gamma Function Inequalities
• The best bounds in Gautschi's inequality
• Monotonicity results and inequalities for the gamma and incomplete gamma functions
• Three classes of logarithmically completely monotonic functions involving gamma and psi functions
• A completely monotonic function involving the divided difference of the psi function and an equivalent inequality involving sums
• Some completely monotonic functions involving the gamma and polygamma functions
• The best bounds in Gautschi-Kershaw inequalities
• What is the Laplace Transform?
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