scholarly journals Complete monotonicity of some functions involving polygamma functions

2010 ◽  
Vol 233 (9) ◽  
pp. 2149-2160 ◽  
Author(s):  
Feng Qi ◽  
Senlin Guo ◽  
Bai-Ni Guo
Keyword(s):  
Complete Monotonicity ◽  
Polygamma Functions

scholarly journals COMPLETE MONOTONICITY OF A FUNCTION INVOLVING THE DIVIDED DIFFERENCE OF PSI FUNCTIONS

2013 ◽  
Vol 88 (2) ◽  
pp. 309-319 ◽  
Author(s):  
FENG QI ◽  
PIETRO CERONE ◽  
SEVER S. DRAGOMIR
Keyword(s):  
Divided Difference ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Complete Monotonicity ◽  
Divided Differences ◽  
Psi Function ◽  
Gamma Functions ◽  
Completely Monotonic ◽  
Polygamma Functions ◽  
Necessary And Sufficient

AbstractNecessary and sufficient conditions are presented for a function involving the divided difference of the psi function to be completely monotonic and for a function involving the ratio of two gamma functions to be logarithmically completely monotonic. From these, some double inequalities are derived for bounding polygamma functions, divided differences of polygamma functions, and the ratio of two gamma functions.

scholarly journals Lower Bound of Sectional Curvature of Manifold of Beta Distributions and Complete Monotonicity of Functions Involving Polygamma Functions

2020 ◽  
Author(s):  
Feng Qi
Keyword(s):  
Lower Bound ◽  
Sectional Curvature ◽  
Sufficient Conditions ◽  
Laplace Transforms ◽  
Complete Monotonicity ◽  
Convolution Theorem ◽  
Open Problems ◽  
Polygamma Functions ◽  
Beta Distributions ◽  
Necessary And Sufficient

In the paper, by convolution theorem for the Laplace transforms and analytic techniques, the author finds necessary and sufficient conditions for complete monotonicity, monotonicity, and inequalities of several functions involving polygamma functions. By these results, the author derives a lower bound of a function related to the sectional curvature of the manifold of the beta distributions. Finally, the author poses several guesses and open problems related to monotonicity, complete monotonicity, and inequalities of several functions involving polygamma functions.

scholarly journals Sharp Inequalities for Polygamma Functions

2015 ◽  
Vol 65 (1) ◽  
Author(s):  
Bai-Ni Guo ◽  
Feng Qi ◽  
Jiao-Lian Zhao ◽  
Qiu-Ming Luo
Keyword(s):  
Rational Functions ◽  
Complete Monotonicity ◽  
Double Inequality ◽  
Polygamma Function ◽  
Polygamma Functions

AbstractIn the paper, the authors review some inequalities and the (logarithmically) complete monotonicity concerning the gamma and polygamma functions and, more importantly, present a sharp double inequality for bounding the polygamma function by rational functions.

Completely monotonicity of class functions involving the polygamma and related functions

2020 ◽  
pp. 2150064
Author(s):  
B. Ravi ◽  
A. Venakata Lakshmi
Keyword(s):  
Lower Bound ◽  
Zeta Function ◽  
Complete Monotonicity ◽  
Open Problems ◽  
Gamma Functions ◽  
Monotonic Functions ◽  
Completely Monotonic ◽  
Polygamma Functions ◽  
Completely Monotonic Functions ◽  
Monotonic Properties

In this paper, the authors prove some inequalities and completely monotonic properties of polygamma functions. As an application, we give lower bound for the zeta function on natural numbers. Partially, we answer the fifth and sixth open problems listed in [F. Qi and R. P. Agarwal, On complete monotonicity for several classes of functions related to ratios of gamma functions, J. Inequalities Appl. 2019(36) (2019) 42]. We propose two open problems on completely monotonic functions related to polygamma functions.

scholarly journals Complete monotonicity of divided differences of the di- and tri-gamma functions with applications

2016 ◽  
Vol 23 (2) ◽  
Author(s):  
Feng Qi ◽  
Bai-Ni Guo
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Complete Monotonicity ◽  
Divided Differences ◽  
Gamma Functions ◽  
Completely Monotonic ◽  
Polygamma Functions ◽  
Necessary And Sufficient

AbstractIn the paper, we establish necessary and sufficient conditions for two families of functions involving divided differences of the di- and tri-gamma functions to be completely monotonic. Consequently, we derive necessary and sufficient conditions for two families of functions involving the ratio of two gamma functions to be logarithmically completely monotonic. Furthermore, we deduce some inequalities for bounding the ratio of two gamma functions and divided differences of polygamma functions.

Complete monotonicity of entropy production in chemical reaction

1981 ◽  
Vol 46 (2) ◽  
pp. 452-456
Author(s):  
Milan Šolc
Keyword(s):  
Entropy Production ◽  
Equilibrium Constant ◽  
Chemical Reaction ◽  
Relative Entropy ◽  
Order Reaction ◽  
Complete Monotonicity ◽  
First Order Reaction ◽  
First Order ◽  
Completely Monotonic ◽  
Derivatives Of

The successive time derivatives of relative entropy and entropy production for a system with a reversible first-order reaction alternate in sign. It is proved that the relative entropy for reactions with an equilibrium constant smaller than or equal to one is completely monotonic in the whole definition interval, and for reactions with an equilibrium constant larger than one this function is completely monotonic at the beginning of the reaction and near to equilibrium.

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