Results 1 to 10 of about 6,289,082 (227)

A necessary and sufficient condition for sequences to be minimal completely monotonic

Advances in Difference Equations, 2020
In this article, we present a necessary and sufficient condition under which sequences are minimal completely monotonic.
Xi-Feng Wang, Mourad E. H. Ismail, Necdet Batir, S. Guo   +3 more
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A SOLUTION TO QI’S EIGHTH OPEN PROBLEM ON COMPLETE MONOTONICITY

Проблемы анализа, 2021
n this paper, the complete monotonicity of 1/( arctan 𝑥) is proved. This problem was posted by F. Qi and R. P. Agarwal as the eighth open problem of collection of eight open problems.
A. Venkata Lakshmi
doaj   +1 more source

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
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Sharp bounds for a ratio of the q-gamma function in terms of the q-digamma function

Journal of Inequalities and Applications, 2021
In the present paper, we introduce sharp upper and lower bounds to the ratio of two q-gamma functions Γ q ( x + 1 ) / Γ q ( x + s ) ${\Gamma }_{q}(x+1)/{\Gamma }_{q}(x+s)$ for all real number s and 0 < q ≠ 1 $0< q\neq1$ in terms of the q-digamma function.
Faris Alzahrani, Ahmed Salem, Moustafa El-Shahed   +2 more
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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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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
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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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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 .
Zhao Tie-Hong, Chu Yu-Ming
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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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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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