Results 1 to 10 of about 860 (206)
Sums Involving the Digamma Function Connected to the Incomplete Beta Function and the Bessel functions [PDF]
Mathematics, 2023 We calculate some infinite sums containing the digamma function in closed form. These sums are related either to the incomplete beta function or to the Bessel functions.
Juan Luis González-Santander +1 more
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Finite and Infinite Hypergeometric Sums Involving the Digamma Function [PDF]
Mathematics, 2022 We calculate some finite and infinite sums containing the digamma function in closed form. For this purpose, we differentiate selected reduction formulas of the hypergeometric function with respect to the parameters applying some derivative formulas of ...
Juan Luis González-Santander +1 more
doaj +8 more sources
On an Iteration Leading to a q-Analogue of the Digamma Function [PDF]
Journal of Fourier Analysis and Applications, 2013 We show that the q-Digamma function psi_q for ...
Christian Berg, Berg Christian
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New approximations of the gamma function in terms of the digamma function [PDF]
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
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Notes on three conjectures involving the digamma and generalized digamma functions [PDF]
Journal of Inequalities and Applications, 2018 In the paper, we solve one conjecture on an inequality involving digamma function, an open problem, and a conjecture on monotonicity of functions involving generalized digamma function. We also prove a new inequality for digamma function.
Ladislav Matejíčka
doaj +3 more sources
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
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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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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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A certain class of approximations for the $q$-digamma function [PDF]
Rocky Mountain Journal of Mathematics, 2016 In this paper, we derive a class of approximations of the $q$-digamma function $\psi _q(x)$. The infinite family \[ I_a(x;q)=\log [x+a]_q+\frac {q^x\log q}{1-q^x}-\bigg (\frac 12-a\bigg )H(q-1)\log q, \] $a\in [0,1]$; $q>0$, can be used as approximating functions for $\psi _q(x)$, where $[x]_q=(1-q^x)/(1-q)$ and $H(\cdot )$ is the Heaviside step ...
Ahmed Salem
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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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