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Complete monotonicity involving some ratios of gamma functions [PDF]
Journal of Inequalities and Applications, 2017 In this paper, by using the properties of an auxiliary function, we mainly present the necessary and sufficient conditions for various ratios constructed by gamma functions to be respectively completely and logarithmically completely monotonic.
Zhen-Hang Yang, Shen-Zhou Zheng
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Monotonicity and complete monotonicity for continuous-time Markov chains [PDF]
Comptes Rendus. Mathématique, 2006 We analyze the notions of monotonicity and complete monotonicity for Markov Chains in continuous-time, taking values in a finite partially ordered set. Similarly to what happens in discrete-time, the two notions are not equivalent. However, we show that there are partially ordered sets for which monotonicity and complete monotonicity coincide in ...
Paolo Dai Pra +2 more
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Short Remarks on Complete Monotonicity of Some Functions [PDF]
Mathematics, 2020 In this paper, we show that the functions x m | β ( m ) ( x ) | are not completely monotonic on ( 0 , ∞ ) for all m ∈ N , where β ( x ) is the Nielsen’s β -function and we prove the functions x m − 1
Ladislav Matejíčka
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Logarithmically Complete Monotonicity Properties Relating to the Gamma Function [PDF]
Abstract and Applied Analysis, 2011 We prove that the function fα,β(x)=Γβ(x+α)/xαΓ(βx) is strictly logarithmically completely monotonic on (0,∞) if (α,β)∈{( α,β):1/α≤β≤1, α≠1}∪{(α,β ...
Tie-Hong Zhao, Yu-Ming Chu, Hua Wang
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A complete monotonicity property of the multiple gamma function [PDF]
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
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Complete monotonicity related to the k-polygamma functions with applications [PDF]
Advances in Difference Equations, 2019 In this paper, we prove complete monotonicity of some functions involving k-polygamma functions. As an application of the main result, we also give new upper and lower bounds of the k-digamma function.
Li Yin, Jumei Zhang, XiuLi Lin
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A Characterization of Optimal Prefix Codes [PDF]
EntropyA property of prefix codes called strong monotonicity is introduced, and it is proven that for a given source, a prefix code is optimal if and only if it is complete and strongly monotone.
Spencer Congero, Kenneth Zeger
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Complete Monotonicity of Special Functions
, 2015 In this work we prove that if an entire function $f(z)$ is of order strictly less than one and it has only negative zeros, then for each nonnegative integer $k,m$ the real function $\left(-\frac{1}{x}\right)^{m}\frac{d^{k}}{dx^{k}}\left(x^{k+m}\frac{d^{m}}{dx^{m}}\left(\frac{f'(x)}{f(x)}\right)\right)$ is completely monotonic on $(0,\infty ...
R. Zhang
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Logarithmically complete monotonicity of a function related to the Catalan-Qi function [PDF]
Acta Universitatis Sapientiae: Mathematica, 2016 In the paper, the authors find necessary and sufficient conditions such that a function related to the Catalan-Qi function, which is an alternative generalization of the Catalan numbers, is logarithmically complete monotonic.
Qi Feng, Guo Bai -Ni
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The complete monotonicity of the Rayleigh function
Journal of Mathematical Analysis and Applications, 1980 Eguono Obi
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