Results 1 to 10 of about 2,422,350 (276)

Monotonicity properties and bounds for the complete p-elliptic integrals

Journal of Inequalities and Applications, 2018
We generalize several monotonicity and convexity properties as well as sharp inequalities for the complete elliptic integrals to the complete p-elliptic integrals.
Ti-Ren Huang, Shen-Yang Tan, Xiao-Yan Ma, Yu-Ming Chu   +3 more
doaj   +4 more sources

Complete monotonicity involving some ratios of gamma functions [PDF]

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
doaj   +2 more sources

From Inequalities Involving Exponential Functions and Sums to Logarithmically Complete Monotonicity of Ratios of Gamma Functions [PDF]

Journal of Mathematical Analysis and Applications, 2021
Bai-Ni Guo, Feng Qi
exaly   +2 more sources

Complete monotonicity and inequalities related to generalized k-gamma and k-polygamma functions

Journal of Inequalities and Applications, 2020
In this paper, we prove new complete monotonicity properties of some functions related to generalized k-gamma and k-polygamma functions. Applications of the results yield various new inequalities. In the end, double inequalities are constructed involving
Ju-Mei Zhang, Li Yin, Hong-Lian You
doaj   +2 more sources

Strong Bounds for Certain Products Using the Gamma Function and Complete Monotonicity

Journal of Mathematics
Our aim is to provide, using properties of the gamma function and the complete monotonicity of functions, some sharp bounds for the products ∏k=1n‍5k−i/5k, i=1,2,3,4.
Jenică Crînganu, Alina-Mihaela Patriciu   +1 more
doaj   +2 more sources

Some Properties of the Kilbas-Saigo Function

Mathematics, 2021
We characterize the complete monotonicity of the Kilbas-Saigo function on the negative half-line. We also provide the exact asymptotics at −∞, and uniform hyperbolic bounds are derived.
Lotfi Boudabsa, Thomas Simon
doaj   +1 more source

Monotonicity properties for a ratio of finite many gamma functions

Advances in Difference Equations, 2020
In the paper, the authors consider a ratio of finite many gamma functions and find its monotonicity properties such as complete monotonicity, the Bernstein function property, and logarithmically complete monotonicity.
Feng Qi, Dongkyu Lim
doaj   +1 more source

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

Monotonicity and absolute monotonicity for the two-parameter hyperbolic and trigonometric functions with applications

Journal of Inequalities and Applications, 2016
In this paper, we present the monotonicity and absolute monotonicity properties for the two-parameter hyperbolic and trigonometric functions. As applications, we find several complete monotonicity properties for the functions involving the gamma function
Zhen-Hang Yang, Yu-Ming Chu
doaj   +1 more source