Results 11 to 20 of about 9,289 (253)

Remarks on some completely monotonic functions

Journal of Mathematical Analysis and Applications, 2006
Applying the Euler-Maclaurin summation formula, the author proves that for all \(n=1,2,3,...\) and \(x>0\) \[ 1-\frac{x}{2}+\sum_{j=1}^{2m}\frac{B_{2j}}{(2j)!}x^{2j}
Koumandos, S., Koumandos, S.
openaire   +5 more sources

On a Conjecture of Alzer, Berg, and Koumandos

Mathematics, 2020
In this paper, we find a solution of an open problem posed by Alzer, Berg, and Koumandos: determine ( α , m ) ∈ R + × N such that the function x α | ψ ( m ) ( x ) | is completely monotonic on ( 0 , ∞ ) , where ψ (
Ladislav Matejíčka
doaj   +1 more source

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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Bounds for completely monotonic degree of a remainder for an asymptotic expansion of the trigamma function

Arab Journal of Basic and Applied Sciences, 2021
In the paper, the author presents bounds for completely monotonic degree of a remainder for an asymptotic expansion of the trigamma function. This result partially confirms one in a series of conjectures on completely monotonic degrees of remainders of ...
Feng Qi
doaj   +1 more source

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
doaj   +2 more sources

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
doaj   +1 more source

Short Remarks on Complete Monotonicity of Some Functions

Mathematics, 2020
In this paper, we show that the functions x m | β ( m ) ( x ) | are not completely monotonic on ( 0 , ∞ ) for all m ∈ N , where β ( x ) is the Nielsen’s β -function and we prove the functions x m − 1
Ladislav Matejíčka
doaj   +1 more source

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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Compatibilities between continuous semilattices

Karpatsʹkì Matematičnì Publìkacìï, 2021
We define compatibilities between continuous semilattices as Scott continuous functions from their pairwise cartesian products to $\{0,1\}$ that are zero preserving in each variable.
O.Ya. Mykytsey, K.M. Koporkh
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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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