A complete monotonicity property of the gamma function
From MaRDI portal
Publication:1877807
DOI10.1016/j.jmaa.2004.04.026zbMath1046.33001OpenAlexW2077314575MaRDI QIDQ1877807
Publication date: 19 August 2004
Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jmaa.2004.04.026
Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems (26A24) Gamma, beta and polygamma functions (33B15)
Related Items (82)
Some properties of the Schröder numbers ⋮ Approximations for certain hyperbolic functions by partial sums of their Taylor series and completely monotonic functions related to gamma function ⋮ On completely monotone of an arbitrary real parameter function involving the gamma function ⋮ A class of logarithmically completely monotonic functions related to the gamma function with applications ⋮ Monotonic properties for ratio of the generalized (p,k)-polygamma functions ⋮ Complete monotonicity of divided differences of the di- and tri-gamma functions with applications ⋮ A class of logarithmically completely monotonic functions and the best bounds in the first Kershaw's double inequality ⋮ Logarithmically completely monotonic functions concerning gamma and digamma functions ⋮ 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 ⋮ Complete monotonicity of some functions involving polygamma functions ⋮ Complete monotonicity and logarithmically complete monotonicity properties for the gamma and psi functions ⋮ Unnamed Item ⋮ Some properties of central Delannoy numbers ⋮ Integral representations of bivariate complex geometric mean and their applications ⋮ Complete monotonicity involving some ratios of gamma functions ⋮ Logarithmically complete monotonicity of a matrix-parametrized analogue of the multinomial distribution ⋮ Some inequalities for the Bell numbers ⋮ Monotonicity properties of functions related to the psi function ⋮ Integral representations and complete monotonicity related to the remainder of Burnside's formula for the gamma function ⋮ Sharp inequalities related to the volume of the unit ball in \(\mathbb{R}^n\) ⋮ Monotonicity, convexity, and inequalities for functions involving gamma function ⋮ Logarithmically completely monotonic rational functions ⋮ The harmonic and geometric means are Bernstein functions ⋮ Some properties of functions related to the gamma, psi and tetragamma functions ⋮ Logarithmically completely monotonic functions and applications ⋮ INEQUALITIES AND COMPLETE MONOTONICITY FOR THE GAMMA AND RELATED FUNCTIONS ⋮ Complete monotonicity of a function involving the ratio of gamma functions and applications ⋮ Bounds for the ratio of two gamma functions -- from Wendel's and related inequalities to logarithmically completely monotonic functions ⋮ Miscellaneous results related to the Gaussian product inequality conjecture for the joint distribution of traces of Wishart matrices ⋮ A LOGARITHMICALLY COMPLETELY MONOTONIC FUNCTION INVOLVING THE RATIO OF GAMMA FUNCTIONS ⋮ Some inequalities and monotonicity properties associated with the gamma and psi functions ⋮ From inequalities involving exponential functions and sums to logarithmically complete monotonicity of ratios of gamma functions ⋮ Monotonicity, concavity, and inequalities related to the generalized digamma function ⋮ The reciprocal of the weighted geometric mean of many positive numbers is a Stieltjes function ⋮ Analytic computation of digamma function using some new identities ⋮ A complete monotonicity property of the multiple gamma function ⋮ Complete monotonicity of a function involving the gamma function and applications ⋮ A new upper bound in the second Kershaw's double inequality and its generalizations ⋮ Complete monotonicity of functions involving the \(q\)-trigamma and \(q\)-tetragamma functions ⋮ Schur-convexity of the Catalan-Qi function related to the Catalan numbers ⋮ The reciprocal of the weighted geometric mean is a Stieltjes function ⋮ A class of logarithmically completely monotonic functions and the best bounds in the second Kershaw's double inequality ⋮ A comparison theorem for two divided differences and applications to special functions ⋮ Integral representations and complete monotonicity of remainders of the binet and Stirling formulas for the gamma function ⋮ Supplements to a class of logarithmically completely monotonic functions associated with the gamma function ⋮ A new lower bound in the second Kershaw's double inequality ⋮ Three classes of logarithmically completely monotonic functions involving gamma and psi functions ⋮ Some properties of the divided difference of psi and polygamma functions ⋮ Bounds for the ratio of two gamma functions ⋮ Logarithmically completely monotonic functions relating to the gamma function ⋮ Necessary and sufficient conditions for two classes of functions to be logarithmically completely monotonic ⋮ A function involving gamma function and having logarithmically absolute convexity ⋮ Monotonicity properties related to the ratio of two gamma functions ⋮ Some monotonicity properties on \(k\)-gamma function and related inequalities ⋮ A ratio of finitely many gamma functions and its properties with applications ⋮ Completely monotonic ratios of basic and ordinary gamma functions ⋮ Sharp inequalities involving \((n!)^{1/n}\) ⋮ The reciprocal of the geometric mean of many positive numbers is a Stieltjes transform ⋮ A certain function class related to the class of logarithmically completely monotonic functions ⋮ Some complete monotonicity properties for the \((p, q)\)-gamma function ⋮ A class of logarithmically completely monotonic functions and application to the best bounds in the second Gautschi-Kershaw's inequality ⋮ A class of logarithmically completely monotonic functions ⋮ Integral representations of the large and little Schröder numbers ⋮ Some inequalities and monotonicity properties associated with the gamma and psi functions and the BarnesG-function ⋮ Logarithmically complete monotonicity of a function related to the Catalan-Qi function ⋮ A class of logarithmically completely monotonic functions associated with the gamma function ⋮ Logarithmically complete monotonicity of Catalan-Qi function related to Catalan numbers ⋮ REMARKS ON COMPLETE MONOTONICITY OF A FUNCTION INVOLVING THE GAMMA FUNCTION ⋮ Some completely monotonic functions involving the gamma and polygamma functions ⋮ Inequalities and monotonicity properties for the psi (or digamma) function and estimates for the Euler–Mascheroni constant ⋮ 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 and inequalities related to generalized \(k\)-gamma and \(k\)-polygamma functions ⋮ On Burnside type approximation for the gamma function ⋮ Monotonicity properties for a ratio of finite many gamma functions ⋮ Unnamed Item ⋮ Some completely monotonic functions involving polygamma functions and an application ⋮ Some properties of the Fuss-Catalan numbers ⋮ An integral representation, complete monotonicity, and inequalities of the Catalan numbers ⋮ A closed-form expression of a remarkable sequence of polynomials originating from a family of entire functions connecting the Bessel and Lambert functions ⋮ Some logarithmically completely monotonic functions and inequalities for multinomial coefficients and multivariate beta functions
Cites Work
- Error Bounds for Asymptotic Expansions of the Ratio of Two Gamma Functions
- The function (𝑏^{𝑥}-𝑎^{𝑥})/𝑥: Inequalities and properties
- Generalized weighted mean values with two parameters
- The best bounds in Gautschi's inequality
- Note on monotonicity of generalized weighted mean values
- Unnamed Item
- Unnamed Item
- Unnamed Item
This page was built for publication: A complete monotonicity property of the gamma function
