Results 31 to 40 of about 6,291 (196)
Mathematics, 2023 In this paper, the authors review and survey some results published since 2020 about (complete) monotonicity, inequalities, and their necessary and sufficient conditions for several newly introduced functions involving polygamma functions and originating
Feng Qi, Ravi Prakash Agarwal
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Complete monotonicity related to the k-polygamma functions with applications
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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Completely Monotonic and Related Functions: Their Applications [PDF]
Journal of Applied Mathematics, 2014 Completely monotonic and related functions are important function classes inmathematical analysis. It was Bernstein [1] who in 1914 first introduced the notion of completely monotonic function. This year we celebrate its 100th anniversary. In 1921, Hausdorff [2] gave the notion of completely monotonic sequence, which is related to the notion of ...
Senlin Guo +3 more
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The Best Bounds in Gautschi-Kershaw Inequalities
, 2005 By employing the convolution theorem of Laplace transforms, some asymptotic formulas and integral representations of the gamma, psi and polygamma functions, and other analytic techniques, this note provides an alternative proof of a monotonicity and ...
Qi, Feng +5 more
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On the Complete Monotonicity of Rényi Entropy
IEEE Transactions on Information TheoryIn 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. We also investigate concavity of Rényi entropy power and the complete monotonicity of Tsallis entropy.
Hao Wu, Lei Yu 0003, Laigang Guo
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Mathematics, 2023 Hyperbolic complete monotonicity property (HCM) is a way to check if a distribution is a generalized gamma (GGC), hence is infinitely divisible. In this work, we illustrate to which extent the Mittag-Leffler functions Eα,α∈(0,2], enjoy the HCM property ...
Nuha Altaymani, Wissem Jedidi
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, 2006 In the article, the logarithmically complete monotonicity of a class of functions involving the Euler’s gamma function are proved, a class of the first Kershaw type double inequalities are established, and the first Kershaw’s double inequality and ...
Qi, Feng
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International Journal of Analysis and Applications, 2014 The authors find the absolute monotonicity and complete monotonicity of some functions involving trigonometric functions and related to estimates the lower bounds of the first eigenvalue of Laplace operator on Riemannian manifolds.
Feng Qi, Miao-Miao Zheng
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Logarithmically Complete Monotonicity Properties Relating to the Gamma Function
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 of the Gamma Function
, 2004 The function 1/x ln Γ(x+1)−ln x+1 is strictly completely monotonic on (0,∞)
Qi, Feng, Chen, Chao-Ping
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