Results 71 to 80 of about 649 (183)

Monotonicity and positivity of several functions involving ratios and products of polygamma functions

Journal of Inequalities and Applications
Let ψ ( x ) $\psi (x)$ denote the digamma function, that is, the logarithmic derivative of the classical Euler gamma function Γ ( x ) $\Gamma (x)$ . In the paper, the authors discover the monotonic properties of the functions ψ ( n ) ( x ) x ψ ( n + 1 ) (
Feng Qi, Dongkyu Lim, Kwara Nantomah
doaj   +1 more source

Analysis On Simpson's Type Inequalities Through Generalized Convexity with Applications [PDF]

Sahand Communications in Mathematical Analysis
Fractional operators and integral inequalities have become a focal point of research due to their applications in mathematics, physics, engineering, and applied sciences.
Arslan Munir, Artion Kashuri
doaj   +1 more source

On complete monotonicity for several classes of functions related to ratios of gamma functions

Journal of Inequalities and Applications, 2019
Let Γ(x) $\varGamma (x)$ denote the classical Euler gamma function. The logarithmic derivative ψ(x)=[lnΓ(x)]′=Γ′(x)Γ(x) $\psi (x)=[\ln \varGamma (x)]'=\frac{\varGamma '(x)}{ \varGamma (x)}$, ψ′(x) $\psi '(x)$, and ψ″(x) $\psi ''(x)$ are, respectively ...
Feng Qi, Ravi P. Agarwal
doaj   +1 more source

A completely monotonic function involving the gamma and trigamma functions

Kuwait Journal of Science, 2016
In the paper the author provides necessary and sufficient conditions on $a$ for the function\begin{equation*}\frac{1}{2}\ln(2\pi)-x+\biggl(x-\frac{1}{2}\biggr)\ln x-\ln\Gamma(x)+\frac1{12}{\psi'(x+a)}\end{equation*}and its negative to be completely ...
Feng Qi
doaj  

A certain family of infinite series associated with Digamma functions

Journal of Mathematical Analysis and Applications, 1991
The sums of several interesting infinite series were expressed recently in terms of the Psi (or Digamma) functions. The object of this paper is to present a systematic account of these (and of numerous similar or general) series whose sums can be found in the literature in various equivalent forms. Some relevant unifications and further generalizations
Al-Saqabi, B.N, Kalla, S.L, Srivastava, H.M   +2 more
openaire   +2 more sources

A study of Hermite-Hadamard inequalities via Caputo-Fabrizio fractional integral operators using strongly ( s , m ) $(s, m)$ -convex functions in the second sense

Journal of Inequalities and Applications
New ways for comparing and bounding strongly ( s , m ) $(s,m)$ -convex functions using Caputo fractional derivatives and Caputo-Fabrizio integral operators are explored.
Jie Li, Yong Lin, Serap Özcan, Muhammad Shoaib Saleem, Ahsan Fareed Shah   +4 more
doaj   +1 more source

Geometric Nature of the Turánian of Modified Bessel Function of the First Kind

Axioms
This work explores the geometric properties of the Turanian of the modified Bessel function of the first kind (TMBF). Using the properties of the digamma function, we establish conditions under which the normalized TMBF satisfies starlikeness, convexity,
Samanway Sarkar, Dimiter Prodanov, Anish Kumar, Sourav Das   +3 more
doaj   +1 more source

On the positivity of a certain function related with the Digamma function

The Ramanujan Journal, 2023
Abstract In this note, we prove that $$\begin{aligned} \left( \frac{x^n}{1-e^{-x}}\right) ^{(n)}>0 \end{aligned}$$
openaire   +4 more sources

Advanced Hermite-Hadamard-Mercer Type Inequalities with Refined Error Estimates and Applications

Fractal and Fractional
The purpose of this research is to develop a set of Hermite–Hadamard–Mercer-type inequalities that involve different types of fractional integral operators such as classical Riemann–Liouville fractional integral operators.
Arslan Munir, Hüseyin Budak, Artion Kashuri, Loredana Ciurdariu   +3 more
doaj   +1 more source

Accurate Thermodynamic Properties of Ideal Bosons in a Highly Anisotropic 2D Harmonic Potential. [PDF]

Entropy (Basel), 2023
Cheng Z.
europepmc   +1 more source