Monotonicity of a mean related to polygamma functions with an application

DOI10.1186/s13660-016-1155-4zbMath1347.33008OpenAlexW2508220199WikidataQ59466235 ScholiaQ59466235MaRDI QIDQ313567

Zhen-Hang Yang, Shen-Zhou Zheng

Publication date: 12 September 2016

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

Full work available at URL: https://doi.org/10.1186/s13660-016-1155-4

Mathematics Subject Classification ID

Gamma, beta and polygamma functions (33B15) Means (26E60)

Related Items (12)

A class of completely monotonic functions involving the polygamma functions ⋮ Complete monotonicity involving some ratios of gamma functions ⋮ Complete monotonicity and inequalities involving the \(k\)-gamma and \(k\)-polygamma functions ⋮ Some properties of the generalized Gaussian ratio and their applications ⋮ A comparison theorem for two divided differences and applications to special functions ⋮ Some properties of the divided difference of psi and polygamma functions ⋮ A class of completely mixed monotonic functions involving the gamma function with applications ⋮ New properties of the divided difference of psi and polygamma functions ⋮ Complete monotonicity and inequalites involving Gurland's ratios of gamma functions ⋮ Asymptotic expansions for the gamma function in terms of hyperbolic functions ⋮ Some inequalities involving the polygamma functions ⋮ Complete monotonicity and inequalities related to generalized \(k\)-gamma and \(k\)-polygamma functions

Cites Work

• Unnamed Item
• Unnamed Item
• On some properties of digamma and polygamma functions
• 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
• 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
• A class of logarithmically completely monotonic functions and the best bounds in the second Kershaw's double inequality
• Derivatives of generalized means
• Some Extensions of W. Gautschi's Inequalities for the Gamma Function
• Refinements, extensions and generalizations of the second Kershaw's double inequality
• Generalizations of the Logarithmic Mean
• Differential and integral f-means and applications to digamma function
• The best bounds in Gautschi's inequality

This page was built for publication: Monotonicity of a mean related to polygamma functions with an application