From inequalities involving exponential functions and sums to logarithmically complete monotonicity of ratios of gamma functions

DOI10.1016/j.jmaa.2020.124478zbMath1451.33002arXiv2001.02175OpenAlexW3048191627WikidataQ98665306 ScholiaQ98665306MaRDI QIDQ2208266

Bai-Ni Guo, Feng Qi

Publication date: 23 October 2020

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

Full work available at URL: https://arxiv.org/abs/2001.02175

zbMATH Keywords

exponential functiongamma functioninequalitysumratiologarithmically complete monotonicity

Mathematics Subject Classification ID

Gamma, beta and polygamma functions (33B15) Inequalities for sums, series and integrals (26D15)

Related Items (9)

Complete monotonicity for a new ratio of finitely many gamma functions ⋮ Decreasing property and complete monotonicity of two functions constituted via three derivatives of a function involving trigamma function ⋮ Logarithmically complete monotonicity of a matrix-parametrized analogue of the multinomial distribution ⋮ Approximation by multivariate Baskakov-Durrmeyer operators in Orlicz spaces ⋮ Necessary and sufficient conditions for a difference constituted by four derivatives of a function involving trigamma function to be completely monotonic ⋮ A ratio of finitely many gamma functions and its properties with applications ⋮ Completely monotonic ratios of basic and ordinary gamma functions ⋮ Logarithmic convexity and increasing property of the Bernoulli numbers and their ratios ⋮ Some logarithmically completely monotonic functions and inequalities for multinomial coefficients and multivariate beta functions

Uses Software

• DLMF

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Completely monotonic gamma ratio and infinitely divisible H-function of Fox
• Complete monotonicity of multinomial probabilities and its application to Bernstein estimators on the simplex
• Complete monotonicity of a function related to the binomial probability
• A double inequality for the ratio of two non-zero neighbouring Bernoulli numbers
• A complete monotonicity property of the gamma function
• Monotonicity properties for a ratio of finite many gamma functions
• Integral representation of some functions related to the gamma function
• Completely monotonic functions involving the gamma and $q$-gamma functions
• TWO NEW PROOFS OF THE COMPLETE MONOTONICITY OF A FUNCTION INVOLVING THE PSI FUNCTION
• On complete monotonicity of linear combination of finite psi functions
• A LOGARITHMICALLY COMPLETELY MONOTONIC FUNCTION INVOLVING THE RATIO OF GAMMA FUNCTIONS
• Hankel-total positivity of some sequences
• Limit formulas for ratios between derivatives of the gamma and digamma functions at their singularities
• Sharp Inequalities for Polygamma Functions
• A property of logarithmically absolutely monotonic functions and the logarithmically complete monotonicity of a power-exponential function
• Some completely monotonic functions involving the gamma and polygamma functions
• Some properties of functions related to the gamma and psi functions
• Bernstein functions. Theory and applications
• Inequalities: theory of majorization and its applications
• Convex functions and their applications. A contemporary approach

This page was built for publication: From inequalities involving exponential functions and sums to logarithmically complete monotonicity of ratios of gamma functions