Results 31 to 40 of about 2,422,350 (276)
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
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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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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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Other Proofs of Monotonicity for Generalized Weighted Mean Values [PDF]
, 1999 In this article, another two simple and short proofs of monotonicity for the generalized weighted mean values with two parameters are ...
Qi, Feng, Mei, Jia-Qiang, Xu, Sen-Lin
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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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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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Monotonicity and sharp inequalities related to complete $(p,q)$-elliptic integrals of the first kind
Comptes Rendus. Mathématique, 2020 With the aid of the monotone L’Hôpital rule, the authors verify monotonicity of some functions involving complete $(p,q)$-elliptic integrals of the first kind and the inverse of generalized hyperbolic tangent function, derive several sharp inequalities ...
Wang, Fei, Qi, Feng
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