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Journal of Mathematical Analysis and Applications, 2007 Recently, several authors have studied the monotonicity properties of functions such as \(\psi(x)= \Gamma'(x)/\Gamma(x)\,.\) See, for instance, [\textit{H. Alzer, C. Berg}, ``Some classes of completely monotonic functions. II.'' Ramanujan J. 11, 225--248 (2006; Zbl 1110.26015), \textit{N. Batir}, J. Math. Anal. Appl.
Chao-Ping Chen
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Strong Bounds for Certain Products Using the Gamma Function and Complete Monotonicity
Journal of MathematicsOur aim is to provide, using properties of the gamma function and the complete monotonicity of functions, some sharp bounds for the products ∏k=1n5k−i/5k, i=1,2,3,4.
Jenică Crînganu +1 more
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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 ...
Pra, PD, Louis, PY, Minelli, I
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From inequalities involving exponential functions and sums to logarithmically complete monotonicity of ratios of gamma functions [PDF]
Journal of Mathematical Analysis and Applications, 2021 Feng Qi, Bai-Ni Guo
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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 Monotone Quasiconcave Duality [PDF]
Mathematics of Operations Research, 2011 We introduce a notion of complete monotone quasiconcave duality, motivated by some economic applications. We show that this duality holds for important classes of quasiconcave functions.
Cerreia Vioglio, Simone +3 more
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On the Composition of Completely Monotonic Functions and Completely Monotonic Sequences and Related Questions [PDF]
Journal of the London Mathematical Society, 1983 The authors answer several previously open questions about c.m. (completely monotonic) sequences and functions. (1) If W(x) is c.m. on \([a,\infty)\) and \(\{\Delta x_ k\}\) is c.m. with \(x_ 0\geq a,\) then \(\{W(x_ k)\}_ 0^{\infty}\) is c.m. Also, the sequence \(\{\mu_ k^{\lambda}\},\quad\mu_ 0=1,\quad\mu_ k>0,\quad k=1,2,...,\) is c.m.
Lorch, Lee, Newman, Donald J.
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Monotonicity properties for a ratio of finite many gamma functions
Advances in Difference Equations, 2020 In the paper, the authors consider a ratio of finite many gamma functions and find its monotonicity properties such as complete monotonicity, the Bernstein function property, and logarithmically complete monotonicity.
Feng Qi, Dongkyu Lim
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Some Properties of the Kilbas-Saigo Function
Mathematics, 2021 We characterize the complete monotonicity of the Kilbas-Saigo function on the negative half-line. We also provide the exact asymptotics at −∞, and uniform hyperbolic bounds are derived.
Lotfi Boudabsa, Thomas Simon
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