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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
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Some completely monotonic functions involving the $q$-gamma function [PDF]

Mathematical Inequalities & Applications, 2010
We present some completely monotonic functions involving the $q$-gamma function that are inspired by their analogues involving the gamma function.Comment: 8 ...
Gao, Peng
core   +3 more sources

Decreasing and complete monotonicity of functions defined by derivatives of completely monotonic function involving trigamma function

Demonstratio Mathematica
In this study, using convolution theorem of the Laplace transforms, a monotonicity rule for the ratio of two Laplace transforms, Bernstein’s theorem for completely monotonic functions, and other analytic techniques, the authors verify decreasing property
Yin Hong-Ping, Han Ling-Xiong, Qi Feng
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Logarithmically completely monotonic rational functions

Automatica, 2023
This paper studies the class of logarithmically completely monotonic (LCM) functions. These functions play an important role in characterising externally positive linear systems which find applications in important control problems such as non-overshooting reference tracking.
Taghavian, Hamed, Drummond, Ross, Johansson, Mikael   +2 more
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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
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Dunkl completely monotonic functions [PDF]

Journal of Difference Equations and Applications, 2017
We introduce the notion of Dunkl completely monotonic functions on $\left(- , \right), >0$. We establish a restrictive version of the analogue of Schoenberg's theorem in Dunkl setting.
Khaled Mehrez, Jamel El Kamel
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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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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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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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