Complete monotonicity involving some ratios of gamma functions

DOI10.1186/s13660-017-1527-4zbMath1372.33002OpenAlexW2760856704WikidataQ42704486 ScholiaQ42704486MaRDI QIDQ2410511

Zhen-Hang Yang, Shen-Zhou Zheng

Publication date: 18 October 2017

Published in: Journal of Inequalities and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13660-017-1527-4

zbMATH Keywords

gamma functioncompletely monotonic functionpsi functionlogarithmically completely monotonic function

Mathematics Subject Classification ID

Gamma, beta and polygamma functions (33B15) Monotonic functions, generalizations (26A48) Exponential and trigonometric functions (33B10)

Related Items (14)

Monotonicity, convexity, and inequalities for functions involving gamma function ⋮ Some properties of the generalized Gaussian ratio and their applications ⋮ Delta complete monotonicity and completely monotonic degree on time scales ⋮ Asymptotic expansions of Gurland's ratio and sharp bounds for their remainders ⋮ A class of completely mixed monotonic functions involving the gamma function with applications ⋮ New properties of the divided difference of psi and polygamma functions ⋮ 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 ⋮ Asymptotic expansions for the gamma function in terms of hyperbolic functions ⋮ On complete monotonicity for several classes of functions related to ratios of gamma functions ⋮ Some completely monotonic functions involving the polygamma functions ⋮ Complete monotonicity of the remainder of the asymptotic series for the ratio of two gamma functions ⋮ A class of strongly completely monotonic functions related to gamma function

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Monotonicity and absolute monotonicity for the two-parameter hyperbolic and trigonometric functions with applications
• Monotonicity of a mean related to polygamma functions with an application
• Bounds for the ratio of two gamma functions
• A class of logarithmically completely monotonic functions and application to the best bounds in the second Gautschi-Kershaw's inequality
• Properties and applications of a function involving exponential functions
• Completely monotonic functions associated with the gamma function and its q-analogues
• 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
• Wendel's and Gautschi's inequalities: refinements, extensions, and a class of logarithmically completely monotonic functions
• A class of logarithmically completely monotonic functions and the best bounds in the second Kershaw's double inequality
• Gurland's ratio for the gamma function
• 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
• Completely monotonic functions involving the gamma and $q$-gamma functions
• On Gamma Function Inequalities
• Stolarsky's Inequality with General Weights
• Two logarithmically completely monotonic functions connected with gamma function
• On some inequalities for the gamma and psi functions
• What is the Laplace Transform?
• Inequalities: theory of majorization and its applications

This page was built for publication: Complete monotonicity involving some ratios of gamma functions