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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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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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Comptes Rendus. Mathématique, 2023 In this paper, we introduce some monotonicity rules for the ratio of integrals. Furthermore, we demonstrate that the function $-T_{\nu ,\alpha ,\beta }(s)$ is completely monotonic in $s$ and absolutely monotonic in $\nu $ if and only if $\beta \ge 1 ...
Mao, Zhong-Xuan, Tian, Jing-Feng
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On the Complete Monotonicity of Rényi Entropy [PDF]
IEEE Transactions on Information Theory, 2023 In this paper, we investigate the complete monotonicity of Rényi entropy along the heat flow. We confirm this property for the order of derivative up to 4, when the order of Rényi entropy is in certain regimes.
Haoxiang Wu, Lei Yu, Laigang Guo
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Complete monotonicity of some functions involving k-digamma function with application [PDF]
Journal of Mathematical Inequalities, 2021 We present several complete monotonicity properties involving k -digamma function with single parameter. These established results provide a k -generalization for the known results obtained by Burić and Elezović in [5]. Finally, we give an application to
Li Yin, Li-Guo Huang, Xiuli Lin
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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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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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On complete monotonicity of three parameter Mittag-Leffler function [PDF]
Applicable Analysis and Discrete Mathematics, 2020 Using the Bernstein theorem we prove the complete monotonicity of the three parameter Mittag?Leffler function E??,? (?w) for w ? 0 and suitably constrained parameters ?, ? and ?.
K. Górska +3 more
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