A class of logarithmically completely monotonic functions and the best bounds in the first Kershaw's double inequality

DOI10.1016/j.cam.2006.09.005zbMath1113.33004OpenAlexW2036032107MaRDI QIDQ2370705

Feng Qi

Publication date: 29 June 2007

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.2006.09.005

zbMATH Keywords

gamma functionextensiongeneralizationrefinementlogarithmically completely monotonic functionopen problembest boundJ.G. Wendel's inequalitythe first Kershaw's double inequality

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 (23)

Complete monotonicity of divided differences of the di- and tri-gamma functions with applications ⋮ Monotonicity and absolute monotonicity for the two-parameter hyperbolic and trigonometric functions with applications ⋮ Wendel's and Gautschi's inequalities: refinements, extensions, and a class of logarithmically completely monotonic functions ⋮ Monotonicity of a mean related to polygamma functions with an application ⋮ The Function (b x − a x )∕x: Ratio’s Properties ⋮ Necessary and sufficient conditions for a class of functions and their reciprocals to be logarithmically completely monotonic ⋮ Complete monotonicity involving some ratios of gamma functions ⋮ A class of logarithmically completely monotonic functions associated with a gamma function ⋮ On some properties of the gamma function ⋮ Logarithmically complete monotonicity properties relating to the gamma function ⋮ Bounds for the ratio of two gamma functions -- from Wendel's and related inequalities to logarithmically completely monotonic functions ⋮ A new upper bound in the second Kershaw's double inequality and its generalizations ⋮ A comparison theorem for two divided differences and applications to special functions ⋮ Supplements to a class of logarithmically completely monotonic functions associated with the gamma function ⋮ 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 class of logarithmically completely monotonic functions and application to the best bounds in the second Gautschi-Kershaw's inequality ⋮ 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 complete monotonicity for several classes of functions related to ratios of gamma functions ⋮ Complete monotonicity of the remainder of the asymptotic series for the ratio of two gamma functions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Completely monotonic and related functions
• A complete monotonicity property of the gamma function
• Integral representation of some functions related to the gamma function
• Inequalities for Generalized Weighted Mean Values of Convex 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
• Completely monotonic functions involving the gamma and $q$-gamma functions
• FOUR LOGARITHMICALLY COMPLETELY MONOTONIC FUNCTIONS INVOLVING GAMMA FUNCTION
• On Gamma Function Inequalities
• On infinitely divisible matrices, kernels, and functions
• Generalized weighted mean values with two parameters
• The best bounds in Gautschi's inequality
• Monotonicity results and inequalities for the gamma and incomplete gamma functions
• Note on monotonicity of generalized weighted mean values
• Some completely monotonic functions involving the gamma and polygamma functions
• The best bounds in Gautschi-Kershaw inequalities
• What is the Laplace Transform?

This page was built for publication: A class of logarithmically completely monotonic functions and the best bounds in the first Kershaw's double inequality