Results 11 to 20 of about 813 (192)

Monotonicity properties on k-digamma function and its related inequalities [PDF]

Journal of Mathematical Inequalities, 2020
Summary: In this work, we give some monotonicity properties of \(k\)-analogues of digamma and polygamma functions and then we obtain some inequalities related to these functions. At last, we give a harmonic mean inequality for the \(k\)-digamma function for all positive real values of \(k\) and \(x\).
Emrah Yıldırım
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A logarithmic estimate for harmonic sums and the digamma function, with an application to the Dirichlet divisor problem [PDF]

Journal of Inequalities and Applications, 2019
Let Hn=∑r=1n1/r $H_{n} = \sum_{r=1}^{n} 1/r$ and Hn(x)=∑r=1n1/(r+x) $H_{n}(x) = \sum_{r=1}^{n} 1/(r+x)$. Let ψ(x) $\psi(x)$ denote the digamma function. It is shown that Hn(x)+ψ(x+1) $H_{n}(x) + \psi(x+1)$ is approximated by 12logf(n+x) $\frac{1}{2}\log ...
G. J. O. Jameson
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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,
Emrah Yıldırım, İncı Ege
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Analytic computations of digamma function using some new identities [PDF]

Journal of Applied Mathematics, Statistics and Informatics, 2018
Abstract Motivated by the substantial development in the theory of digamma function, we derive some new identities for the digamma function. These new identities enable us to compute the values of the digamma function for fractional orders in an analogous manner.
M. I. Qureshi, Mohd Shadab
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Construction of the Digamma Function by Derivative Definition [PDF]

, 2008
The Digamma and Polygamma functions are important tools in mathematical physics, not only for its many properties but also for the applications in statistical mechanics and stellar evolution. In many textbooks is found its develop almost by the same procedure. In this paper expressions for the Digamma and Polygamma functions, in terms of hypergeometric
Michael Morales
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Inequalities involving the gamma and digamma functions [PDF]

, 2018
We improve the upper bounds of the following inequalities proved in [H. Alzer and N. Batir, Monotonicity properties of the gamma function, Appl. Math. Letters, 20(2007), 778-781]. \begin{equation*} exp\left(-\frac{1}{2} \left(x+\frac{1}{3}\right)\right)
Necdet Batır
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THE MODULAR RELATION AND THE DIGAMMA FUNCTION

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.
Kalyan Chakraborty, Shigeru Kanemitsu, X.-H. Wang   +2 more
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On an integral involving the digamma function [PDF]

, 2012
We consider several possible approaches to evaluating an integral involving the digamma function and a related logarithmic series.
Donal F. Connon
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Complete Monotonicity property for two functions related to the q-digamma function [PDF]

Journal of Mathematical Inequalities, 2019
Summary: In this paper, the complete monotonicity property for two functions involving the \(q\)-digamma function are proven for all positive real \(q\) and exploited to establish some sharp inequalities for the \(q\)-gamma, \(q\)-digamma and \(q\)-polygamma functions. Comparisons between our results with previous results are provided.
Ahmed Salem, Faris Alzahrani
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Sharp bounds for a ratio of the q-gamma function in terms of the q-digamma function

Journal of Inequalities and Applications, 2021
In the present paper, we introduce sharp upper and lower bounds to the ratio of two q-gamma functions Γ q ( x + 1 ) / Γ q ( x + s ) ${\Gamma }_{q}(x+1)/{\Gamma }_{q}(x+s)$ for all real number s and 0 < q ≠ 1 $0< q\neq1$ in terms of the q-digamma function.
Faris Alzahrani, Ahmed Salem, Moustafa El-Shahed   +2 more
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