Results 21 to 30 of about 6,291 (196)
Increasing property and logarithmic convexity of functions involving Dirichlet lambda function
Demonstratio Mathematica, 2023 In this article, with the help of an integral representation of the Dirichlet lambda function, by means of a monotonicity rule for the ratio of two integrals with a parameter, and by virtue of complete monotonicity and another property of an elementary ...
Qi Feng, Lim Dongkyu
doaj +1 more source
Logarithmically completely monotonic rational functions
Automatica, 2023 This paper studies the class of logarithmically completely monotonic (LCM) functions. These functions play an important role in characterising externally positive linear systems which find applications in important control problems such as non-overshooting reference tracking.
Taghavian, Hamed +2 more
openaire +4 more sources
Constructing models for spherical and elliptical densities
Dependence Modeling, 2023 The article provides construction algorithms for consistent model classes of continuous spherical and elliptical distributions. The algorithms are based on characterization theorems for consistent families of generator functions.
Liebscher Eckhard
doaj +1 more source
A complete monotonicity property of the multiple gamma function
Comptes Rendus. Mathématique, 2020 We consider the following functions \[ f_n(x)=1-\ln x+\frac{\ln G_n(x+1)}{x} \text{ and }g_n(x)=\frac{\@root x \of {G_n(x+1)}}{x},\; x\in (0,\infty ),\; n\in \mathbb{N}, \] where $G_n(z)=\left(\Gamma _n(z)\right)^{(-1)^{n-1}}$ and $\Gamma _n$ is the ...
Das, Sourav
doaj +1 more source
A combinatorial proof of the Gaussian product inequality beyond the MTP2 case
Dependence Modeling, 2022 A combinatorial proof of the Gaussian product inequality (GPI) is given under the assumption that each component of a centered Gaussian random vector X=(X1,…,Xd){\boldsymbol{X}}=\left({X}_{1},\ldots ,{X}_{d}) of arbitrary length can be written as a ...
Genest Christian, Ouimet Frédéric
doaj +1 more source
A SOLUTION TO QI’S EIGHTH OPEN PROBLEM ON COMPLETE MONOTONICITY
Проблемы анализа, 2021 n this paper, the complete monotonicity of 1/( arctan 𝑥) is proved. This problem was posted by F. Qi and R. P. Agarwal as the eighth open problem of collection of eight open problems.
A. Venkata Lakshmi
doaj +1 more source
A class of completely monotonic functions involving the polygamma functions
Journal of Inequalities and Applications, 2022 Let Γ ( x ) $\Gamma (x)$ denote the classical Euler gamma function. We set ψ n ( x ) = ( − 1 ) n − 1 ψ ( n ) ( x ) $\psi _{n}(x)=(-1)^{n-1}\psi ^{(n)}(x)$ ( n ∈ N $n\in \mathbb{N}$ ), where ψ ( n ) ( x ) $\psi ^{(n)}(x)$ denotes the nth derivative of the
Li-Chun Liang, Li-Fei Zheng, Aying Wan
doaj +1 more source
Directional Shift-Stable Functions
Mathematics, 2021 Recently, some new types of monotonicity—in particular, weak monotonicity and directional monotonicity of an n-ary real function—were introduced and successfully applied.
Radko Mesiar, Andrea Stupňanová
doaj +1 more source
Some Properties of the Fuss–Catalan Numbers
Mathematics, 2018 In the paper, the authors express the Fuss⁻Catalan numbers as several forms in terms of the Catalan⁻Qi function, find some analytic properties, including the monotonicity, logarithmic convexity, complete monotonicity, and minimality, of the ...
Feng Qi, Pietro Cerone
doaj +1 more source
Complete monotonicity of some entropies [PDF]
Periodica Mathematica Hungarica, 2016 It is well-known that the Shannon entropies of some parameterized probability distributions are concave functions with respect to the parameter. In this paper we consider a family of such distributions (including the binomial, Poisson, and negative binomial distributions) and investigate the Shannon, Rényi, and Tsallis entropies of them with respect to
openaire +3 more sources