Results 11 to 20 of about 860 (206)

A completely monotonic function involving q-gamma and q-digamma functions [PDF]

Journal of Approximation Theory, 2012
The author proves the completely monotonicity of functions involving \(q\)-gamma and \(q\)-digamma functions, for \(q>0\). The obtained results give new inequalities for \(q\)-gamma functions as well as generalize other obtained results.
Ahmed Salem
exaly   +3 more sources

Monotonicity, concavity, and inequalities related to the generalized digamma function [PDF]

Advances in Difference Equations, 2018
In this paper, we establish a concave theorem and some inequalities for the generalized digamma function. Hence, we give complete monotonicity property of a determinant function involving all kinds of derivatives of the generalized digamma function.
Li Yin, Li-Guo Huang, Xiu-Li Lin, Yong-Li Wang   +3 more
doaj   +2 more sources

THE MODULAR RELATION AND THE DIGAMMA FUNCTION [PDF]

Kyushu Journal of Mathematics, 2011
In this paper we shall locate a class of fundamental identities for the gamma function and trigonometric functions in the chart of functional equations for the zeta- functions as a manifestation of the underlying modular relation. We use the beta-transform but not the inverse Heaviside integral.
CHAKRABORTY, K., KANEMITSU, S., WANG, X.-H.   +2 more
openaire   +3 more sources

Transcendental values of the digamma function [PDF]

Journal of Number Theory, 2007
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ram Murty, M., Saradha, N.
openaire   +3 more sources

New Approximation Formula of Digamma Function with Bounded Remainder [PDF]

Mathematics
This study establishes the new approximation formula for the Digamma function ψ(s)=lns−12s−112ss2+θ(s ...
Mansour Mahmoud, Abdulaziz S. Alofi, Mohammed A. Zurayyir   +2 more
doaj   +2 more sources

Sharp bounds for gamma and digamma function arising from Burnside's formula [PDF]

Journal of Numerical Analysis and Approximation Theory, 2010
The main aim of this paper is to improve the Burnside's formula for approximating the factorial function. We prove the complete monotonicity of a function involving the gamma function to establish new lower and upper sharp bounds for the gamma and ...
Cristinel Mortici
doaj   +4 more sources

New Closed Form Estimators for the Beta Distribution

Mathematics, 2023
In this paper, we detail closed form estimators for beta distribution that are simpler than those proposed by Tamae, Irie and Kubokawa. The proposed estimators are shown to have smaller asymptotic variances and smaller asymptotic covariances compared to ...
Victor Mooto Nawa, Saralees Nadarajah
doaj   +1 more source

New Inequalities for Gamma and Digamma Functions [PDF]

Journal of Applied Mathematics, 2014
By using the mean value theorem and logarithmic convexity, we obtain some new inequalities for gamma and digamma functions.
M. R. Farhangdoost, M. Kargar Dolatabadi
openaire   +4 more sources

On k-analogues of digamma and polygamma functions [PDF]

Journal of Classical Analysis, 2018
Summary: In this work, we obtain some integral representations of \(k\)-analogue of classical digammafunction \(\Psi(x)\). Then by using the concepts of neutrix and neutrix limit, we generalize the \(k\)-digamma function \(\Psi_k(x)\) and the \(k\)-polygamma function \(\Psi_k^{(r)}(x)\) for all real values of \(x\), \(r\in \mathbb N\) and \(k>0\). Also,
Yıldırım, Emrah, Ege, İncı
openaire   +1 more source

A Rational Approximant for the Digamma Function [PDF]

Numerical Algorithms, 2003
Power series representations for special functions are computationally satisfactory only in the vicinity of the expansion point. Thus, it is an obvious idea to use instead Padé approximants or other rational functions constructed from sequence transformations.
openaire   +2 more sources