A class of logarithmically completely monotonic functions associated with a gamma function
type: Item
instance of: scholarly article
title: A class of logarithmically completely monotonic functions associated with a gamma function
zbMATH Open document ID: 1210.33004
DOI: 10.1155/2010/392431
author: Tiehong Zhao
author: Yu-Ming Chu
published in: Journal of Inequalities and Applications
publication date: 2011-02-08T00:00:00Z
full work available at URL: https://eudml.org/doc/229794
review text: The authors study the log complete monotonicity of the functions j\(G(x)= [e^x\Gamma(x+ a)]/(x+ b)^{x+ b}\), and \(1/G(x)\), where \(x> 0\). The proofs are based among others on integral representations, as well as inequalities for the digamma function.
reviewed by: József Sándor
Mathematics Subject Classification ID: 33B15
Mathematics Subject Classification ID: 26A48
zbMATH DE Number: 5847770
zbMATH Keywords: Euler gamma function
zbMATH Keywords: complete monotonicity
Wikidata QID: Q59253035
MaRDI profile type: Publication
OpenAlex ID: W2154958863
cites work: Q4716292
cites work: THE GEOMETRIC CONVEXITY OF A FUNCTION INVOLVING GAMMA FUNCTION WITH APPLICATIONS
cites work: A double inequality for gamma function
cites work: Monotonic and logarithmically convex properties of a function involving gamma functions
cites work: Q3511823
cites work: Q3535331
cites work: Q5447563
cites work: Q5717247
cites work: TWO NEW PROOFS OF THE COMPLETE MONOTONICITY OF A FUNCTION INVOLVING THE PSI FUNCTION
cites work: Some properties of functions related to the gamma and psi functions
cites work: A completely monotonic function involving the divided difference of the psi function and an equivalent inequality involving sums
cites work: Q4678393
cites work: Q3155729
cites work: Inequalities and monotonicity for the ratio of gamma functions.
cites work: Monotonicity results and inequalities for the gamma and incomplete gamma functions
cites work: Some inequalities of the incomplete gamma and related functions
cites work: Inequalities for the Incomplete Gamma and Related Functions
cites work: Some Gamma Function Inequalities
cites work: On some inequalities for the gamma and psi functions
cites work: A monotoneity property of the gamma function
cites work: Some Extensions of W. Gautschi's Inequalities for the Gamma Function
cites work: Logarithmic convexity and inequalities for the gamma function
cites work: Some classes of completely monotonic functions. II
cites work: Sharp inequalities for the digamma and polygamma functions
cites work: Monotonicity properties of the gamma function
cites work: INEQUALITIES INVOLVING GAMMA AND PSI FUNCTIONS
cites work: On some properties of the Gamma function
cites work: On Gamma Function Inequalities
cites work: Completely monotonic functions associated with the gamma function and its q-analogues
cites work: On Kolmogorov-type inequalities for functions defined on a semiaxis
cites work: Some monotonicity properties and characterizations of the gamma function
cites work: Two logarithmically completely monotonic functions connected with gamma function
cites work: Q5292860
cites work: Logarithmically completely monotonic functions concerning gamma and digamma functions
cites work: A class of logarithmically completely monotonic functions and the best bounds in the first Kershaw's double inequality
cites work: Q5467184
cites work: Logarithmically completely monotonic functions relating to the gamma function
cites work: Complete monotonicity properties for a ratio of gamma functions
cites work: Q4378267
cites work: SOME COMPLETELY MONOTONIC FUNCTIONS INVOLVING THE GAMMA AND POLYGAMMA FUNCTIONS
cites work: FOUR LOGARITHMICALLY COMPLETELY MONOTONIC FUNCTIONS INVOLVING GAMMA FUNCTION
cites work: Further Inequalities for the Gamma Function
cites work: The best bounds in Gautschi's inequality
cites work: The best bounds in Gautschi-Kershaw inequalities
cites work: Q5433690
description: scientific article; zbMATH DE number 5847770