Results 11 to 20 of about 2,821,192 (174)

Estimating the polygamma functions for negative integers [PDF]

Journal of Inequalities and Applications, 2013
Abstract The polygamma functions ψ ( r ) ( x ) are defined for all x
Salem, Ahmed, Kilicman, Adem
openaire   +2 more sources

Analytical Properties of k-Generalized Digamma and Polygamma Functions Derived From Dilcher-Type Gamma Functions

Journal of Mathematics
This study presents a detailed investigation into the analytical properties of the generalized Gamma function introduced by Dilcher. We establish a fundamental recurrence relation and derive novel reflection formula for this generalized function ...
Gregory Abe-I-Kpeng, Mohammed Muniru Iddrisu, Kwara Nantomah   +2 more
doaj   +2 more sources

Turán type inequalities for p-polygamma functions

Le Matematiche, 2013
The aim of this paper is to establish new Turán-type inequalities involving the p−polygamma functions.
Faton Z Merovci
doaj   +2 more sources

Some completely monotonic functions involving the polygamma functions [PDF]

Journal of Inequalities and Applications, 2019
Motivated by existing results, we present some completely monotonic functions involving the polygamma functions.
Peng Gao
doaj   +3 more sources

Complete monotonicity related to the k-polygamma functions with applications [PDF]

Advances in Difference Equations, 2019
In this paper, we prove complete monotonicity of some functions involving k-polygamma functions. As an application of the main result, we also give new upper and lower bounds of the k-digamma function.
Li Yin, Jumei Zhang, XiuLi Lin
doaj   +3 more sources

Some New Inequalities for the Gamma and Polygamma Functions

Symmetry
In this paper, we present some new symmetric bounds for the gamma and polygamma functions. For this goal, we present two functions involving gamma and polygamma functions and we investigate their complete monotonicity. Also, we investigate their completely monotonic degrees.
Waad Al Sayed, Hesham Moustafa
openaire   +2 more sources

A Completely Monotonic Function Involving Divided Differences of Psi and Polygamma Functions and an Application [PDF]

, 2006
A function involving the divided differences of the psi function and the polygamma functions is proved to be completely monotonic. As an application of this result, the monotonicity and convexity of a function originated from establishing the best ...
Qi, Feng
core   +6 more sources

Chelation Therapy for Rare Earth Element Toxicity: Current Evidence, Challenges and Future Directions. [PDF]

Basic Clin Pharmacol Toxicol
ABSTRACT The accelerating integration of rare earth elements (REEs) in advanced technologies has generated rising concern over human exposure and the attendant toxicological risks. This review presents an up‐to‐date synthesis of current evidence on REE toxicity across multiple exposure pathways, including inhalation, ingestion and occupational contact,
Domingo JL.
europepmc   +2 more sources

New Upper Bounds in the Second Kershaw's Double Inequality and its Generalizations [PDF]

, 2007
In the paper, new upper bounds in the second Kershaw’s double inequality and its generalizations involving the gamma, psi and polygamma functions are established, some known results are ...
Guo, Senlin, Qi, Feng
core   +4 more sources

The Best Bounds in Kershaw's Inequality and Two Completely Monotonic Functions [PDF]

, 2006
A new proof for monotonicity and convexity of a function deduced from Kershaw’s inequality involving the Wallis’ function about the Euler’s gamma function is provided.
Qi, Feng
core   +4 more sources