A Completely Monotonic Function Involving Divided Difference of Psi Function and an Equivalent Inequality Involving Sum [PDF]
, 2006 In this paper, a function involving the divided difference of the psi function is proved to be completely monotonic, a class of inequalities involving sum are founded, and an equivalent relation between the complete monotonicity and one of the class ...
Qi, Feng
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Three Classes of Logarithmically Completely Monotonic Functions Involving Gamma and Psi Functions [PDF]
, 2006 By a simple approach, two classes of functions involving 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 function is showed ...
Qi, Feng
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A Logarithmically Completely Monotonic Function Involving the Gamma Function [PDF]
, 2008 In this paper ,we present some logarithmically completely monotonic functions .
An, Miao-Qing
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Logarithmically Completely Monotonic Ratios of Mean Values and an Application [PDF]
, 2005 In the article, some strictly Logarithmically completely monotonic ratios of mean values are ...
Qi, Feng, Chen, Chao-Ping
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Wendel-Gautschi-Kershaw's Inequalities and Sufficient and Necessary Conditions that a Class of Functions Involving Ratio of Gamma Functions are Logarithmically Completely Monotonic [PDF]
, 2007 In the article, sufficient and necessary conditions that a class of functions involving ratio of Euler’s gamma functions and originating from Wendel-Gautschi-Kershaw’s double inequalities are logarithmically completely monotonic are presented.
Qi, Feng, Guo, Bai-Ni
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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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Fractal and Fractional, 2023 In the paper, the authors find a sufficient and necessary condition for the power-exponential function 1+1xαx to be a Bernstein function, derive closed-form formulas for the nth derivatives of the power-exponential functions 1+1xαx and (1+x)α/x, and ...
Jian Cao +3 more
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Sharp inequalities related to the volume of the unit ball in R n $\mathbb{R}^{n}$
Journal of Inequalities and Applications, 2023 Let Ω n = π n / 2 / Γ ( n 2 + 1 ) $\Omega _{n}=\pi ^{n/2}/\Gamma (\frac{n}{2}+1)$ ( n ∈ N $n \in \mathbb{N}$ ) denote the volume of the unit ball in R n $\mathbb{R}^{n}$ .
Xue-Feng Han, Chao-Ping Chen
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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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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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