A Class of Logarithmically Completely Monotonic Functions Associated with a Gamma Function
Journal of Inequalities and Applications, 2010 We show that the function is strictly logarithmically completely monotonic on if and only if and is strictly logarithmically completely monotonic on if and only if .
Tie-Hong Zhao, Yu-Ming Chu
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Two Approximation Formulas for Bateman’s G-Function with Bounded Monotonic Errors
Mathematics, 2022 Two new approximation formulas for Bateman’s G-function are presented with strictly monotonic error functions and we deduced their sharp bounds. We also studied the completely monotonic (CM) degrees of two functions involving G(r), deducing two of its ...
Mansour Mahmoud, Hanan Almuashi
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Logarithmically completely monotonic functions involving the Generalized Gamma Function
Le Matematiche, 2010 By a simple approach, two classes of functions involving generalization Euler's gamma function and originating from certain problems of traffic flow are proved to be logarithmically completely monotonic and a class of functions involving the psi ...
Faton Merovci, Valmir Krasniqi
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A completely monotonic function involving the gamma and trigamma functions
Kuwait Journal of Science, 2016 In the paper the author provides necessary and sufficient conditions on $a$ for the function\begin{equation*}\frac{1}{2}\ln(2\pi)-x+\biggl(x-\frac{1}{2}\biggr)\ln x-\ln\Gamma(x)+\frac1{12}{\psi'(x+a)}\end{equation*}and its negative to be completely ...
Feng Qi
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Necessary and sufficient conditions for a class of functions and their reciprocals to be logarithmically completely monotonic [PDF]
Journal of Inequalities and Applications, 2011 We prove that the function F α,β (x) = x α Γ β (x)/Γ(βx) is strictly logarithmically completely monotonic on (0, ∞) if and only if (α, β) ∈ {(α, β) : β > 0, β ≥ 2 ...
Lv Yu-Pei, Sun Tian-Chuan, Chu Yu-Ming
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An Approximation Formula for Nielsen’s Beta Function Involving the Trigamma Function
Mathematics, 2022 We prove that the function σ(s) defined by β(s)=6s2+12s+53s2(2s+3)−ψ′(s)2−σ(s)2s5,s>0, is strictly increasing with the sharp bounds ...
Mansour Mahmoud, Hanan Almuashi
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Complete monotonicity involving some ratios of gamma functions
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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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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A Note on Superspirals of Confluent Type
Mathematics, 2020 Superspirals include a very broad family of monotonic curvature curves, whose radius of curvature is defined by a completely monotonic Gauss hypergeometric function.
Jun-ichi Inoguchi +2 more
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Some completely monotonic functions involving the polygamma functions
Journal of Inequalities and Applications, 2019 Motivated by existing results, we present some completely monotonic functions involving the polygamma functions.
Peng Gao
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