Results 91 to 100 of about 860 (206)

Logarithmically completely monotonic functions concerning gamma and digamma functions [PDF]

, 2007
For given real numbers a0, b and c, let Fa, b, c(x)=[(x+1)]1/x(1+a/x)x+b/xc and a, b, c(x)=''(x)+[2+(b+c)x-2x2]/x3+[3a(2a-b)+(6a-b)x+2x2]/(x+a)3 with x(0, ), where (x) and (x) are the well-known Euler gamma function and the psi or digamma function ...
Cheung, WS, Chen, SX, Shou-Xin Chen, Feng Qi, Wing-Sum Cheung, Qi, F   +5 more
core   +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 Class of Logarithmically Completely Monotonic Functions and the Best Bounds in the First Kershaw's Double Inequality [PDF]

, 2006
In the article, the logarithmically complete monotonicity of a class of functions involving the Euler’s gamma function are proved, a class of the first Kershaw type double inequalities are established, and the first Kershaw’s double inequality and ...
Qi, Feng
core   +1 more source

Inequalities for the Double Gamma Function [PDF]

, 2008
We establish various new upper and lower bounds in terms of the classical gamma and digamma functions for the double gamma function (or Barnes G- function)
Batir, Necdet
core   +3 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

Derivatives of the Incomplete Beta Function [PDF]

The incomplete beta function is defined as where Beta(p, q) is the beta function. Dutka (1981) gave a history of the development and numerical evaluation of this function. In this article, an algorithm for computing first and second derivatives of Ix,p,q
James F. Robinson-Cox, Robert J. Boik
core   +1 more source

Some combinatorial series identities associated with the digamma function and harmonic numbers [PDF]

, 2010
The authors develop closed-form sums of several interesting families of series associated with the Digamma (or Psi) function and harmonic numbers. A number of illustrative examples and applications of the main results are also considered.National ...
Wu, T.-C., Tu, S.-T., Srivastava, H.M.
core   +1 more source

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

The Ramanujan Journal
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +2 more sources

Some exponential and trigonometric integrals involving the log gamma function [PDF]

, 2022
This paper considers some integrals where the integrand comprises the log gamma function or the digamma function multiplied by exponential or trigonometric ...
Connon, Donal F.
core   +1 more source

Stirling numbers and inverse factorial series [PDF]

Contributions to Mathematics, 2023
Khristo N. Boyadzhiev
doaj   +1 more source