A complete monotonicity property of the multiple gamma function
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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Inequalities, asymptotic expansions and completely monotonic functions related to the gamma function [PDF]
, 2014 In this paper, we present some completely monotonic functions and asymptotic expansions related to the gamma function. Based on the obtained expansions, we provide new bounds for Γ(x + 1)/Γ(x + 1/2) and Γ(x + 1/2)
Chen, Chao-Ping, Paris, Richard B.
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Completely monotonic ratios of basic and ordinary gamma functions
, 2020 We investigate conditions for logarithmic complete monotonicity of product ratios of gamma and q-gamma functions whose arguments are linear functions of the variable.
Berg, Christian +2 more
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Properties of modified Bessel functions and completely monotonic degrees of differences between exponential and trigamma functions [PDF]
, 2014 In the paper, the author establishes inequalities, monotonicity, convexity, and unimodality for functions concerning the modified Bessel functions of the first kind and compute the completely monotonic degrees of differences between the exponential and ...
Qi, Feng
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Journal of Inequalities and Applications, 2020 Several conjectures posed by Qi on completely monotonic degrees of remainders for the asymptotic formulas of the digamma and trigamma functions are proved.
Ai-Min Xu, Zhong-Di Cen
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Comparison of visual quantities in untrained neural networks
Cell Reports, 2023 Summary: The ability to compare quantities of visual objects with two distinct measures, proportion and difference, is observed even in newborn animals.
Hyeonsu Lee +3 more
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A Class of Logarithmically Completely Monotonic Functions and Their Applications
Journal of Applied Mathematics, 2014 We study the recent investigations on a class of functions which are logarithmically completely monotonic. Two open problems are also presented.
Senlin Guo
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Completely Monotone Functions: A Digest [PDF]
, 2014 To appear in: K. Alladi, G.V. Milovanovic and M. Th. Rassias (Eds.): "Analytic Number Theory, Approximation Theory and Special Functions", Special Volume dedicated to Professor Hari M.
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Series representations of the remainders in the expansions for certain functions with applications [PDF]
, 2016 We present a summary of the series representations of the remainders in the expansions in ascending powers of t of 2/(et+1), sech t and coth t and establish simple bounds for these remainders when t>0.
Chen, Chao-Ping, Paris, Richard B.
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Complete Monotonicity of Functions Connected with the Exponential Function and Derivatives
Abstract and Applied Analysis, 2014 Some complete monotonicity results that the functions ±1/e±t-1 are logarithmically completely monotonic, and that differences between consecutive derivatives of these two functions are completely monotonic, and that the ratios between consecutive ...
Chun-Fu Wei, Bai-Ni Guo
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