Results 11 to 20 of about 14,913 (164)

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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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, Rushan Ziatdinov, Kenjiro T. Miura   +2 more
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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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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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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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A Sufficient and Necessary Condition for the Power-Exponential Function ${\left(1+\frac{1}{x}\right)}^{\alpha x}$ to Be a Bernstein Function and Related nth Derivatives

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, Bai-Ni Guo, Wei-Shih Du, Feng Qi   +3 more
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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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Monotonicity and complete monotonicity of some functions involving the modified Bessel functions of the second kind

Comptes Rendus. Mathématique, 2023
In this paper, we introduce some monotonicity rules for the ratio of integrals. Furthermore, we demonstrate that the function $-T_{\nu ,\alpha ,\beta }(s)$ is completely monotonic in $s$ and absolutely monotonic in $\nu $ if and only if $\beta \ge 1 ...
Mao, Zhong-Xuan, Tian, Jing-Feng
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Qi’s conjectures on completely monotonic degrees of remainders of asymptotic formulas of di- and trigamma functions

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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On Some Complete Monotonicity of Functions Related to Generalized k−Gamma Function

Journal of Mathematics, 2021
In this paper, we presented two completely monotonic functions involving the generalized k−gamma function Γkx and its logarithmic derivative ψkx, and established some upper and lower bounds for Γkx in terms of ψkx.
Hesham Moustafa, Hanan Almuashi, Mansour Mahmoud   +2 more
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