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Some Properties and Expansions Associated With the q-Digamma Function

Quaestiones Mathematicae, 2013
This paper is devoted to derive some properties and expansions associated with the q-digamma function. The Newton series which is consisting of terms of forward difference operator, is established for the q-digamma function. The maltiplication formula of
Ahmed Salem
exaly   +1 more source

Estimating Gamma Function by Digamma Function

Mathematical and Computer Modelling, 2010
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Cristinel Mortici
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FUNCTIONAL INEQUALITIES FOR THE q-DIGAMMA FUNCTION

Acta Mathematica Hungarica, 2022
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Alzer, H., Salem, A.
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Infinite Family of Approximations of the Digamma Function

Mathematical and Computer Modelling, 2006
Let \(\textstyle \Psi(x):=\frac{\Gamma^{\prime}(x)}{\Gamma(x)}\) be the psi or digamma function. The authors construct an infinite number of approximations for \(\Psi(x)\), \(x\in (0,\infty)\), denoted as \(\{I_{a}, a\in[0,1]\}\), where \(I_{a}(x)=\ln(x+a)-\frac{1}{x}\).
Isa Muqattash, Mohammed Yahdi
exaly   +2 more sources

New Approximations of the Gamma Function in Terms of the Digamma Function

Applied Mathematics Letters, 2010
The author proves the following asymptotic formula \[ \Gamma(x)\approx\sqrt{2\pi}e^{-b}\,(x+b)^x\,\exp\big(-x-\frac{1}{2}\,\psi(x+c)\big),\;\;\text{as}\,\,x\to\infty,\;\;x\in\mathbb{N}\,, \] where \(\Gamma(x)\) is Euler's gamma function and \(\psi(x)=\frac{\Gamma^{\prime}(x)}{\Gamma(x)}\). Moreover, optimal values of parameters \(b,\,c\) are calculated
Cristinel Mortici
exaly   +4 more sources

Mean Value Inequalities for the Digamma Function

Analysis Mathematica, 2023
Let \(\psi\) be the digamma function. The authors give an upper estimate for \((b-a)\psi(\sqrt{ab})\) and a lower estimate for \((b-a)\psi((a+b)/2)\) in terms of the logarithmic mean \(L(a,b):=(b-a)/\log(b/a)\). \par For all real numbers \(a\) and \(b\) with \(b>a\ge \alpha_0\) we have \[ (b-a)\psi(\sqrt{ab})a>0\) we have \[\left(L(a,b)-a\right)\psi(a)+
Alzer, H., Kwong, M. K.
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A Fast Algorithm for Computing the Digamma Function

Automation and Remote Control, 2022
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Some Inequalities for the Trigamma Function in Terms of the Digamma Function [PDF]

Applied Mathematics and Computation, 2015
In the paper, the authors establish three kinds of double inequalities for the trigamma function in terms of the exponential function to powers of the digamma function. These newly established inequalities extend some known results. The method in the paper utilizes some facts from the asymptotic theory and is a natural way to solve problems for ...
Cristinel Mortici, Feng Qi
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On Some Properties of Digamma and Polygamma Functions

Journal of Mathematical Analysis and Applications, 2007
The author proves some interesting inequalities involving the logarithmic derivative of the gamma function \(\psi(x)=\frac{\Gamma^{\prime}(x)}{\Gamma(x)}\), and its derivatives \(\psi_{n}(x)=\psi^{(n)}(x),\;n=1,2,3,\ldots\), known as polygamma functions.
Necdet Batir
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A Completely Monotonic Function Involving q-Gamma and q-Digamma Functions

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
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