Results 1 to 10 of about 610 (144)
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
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Finite and Infinite Hypergeometric Sums Involving the Digamma Function
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
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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 +2 more
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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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Complete monotonicity of some functions involving k-digamma function with application [PDF]
Journal of Mathematical Inequalities, 2021 Summary: We present several complete monotonicity properties involving \(k\)-digamma function with single parameter. These established results provide a \(k\)-generalization for the known results obtained by \textit{T. Burić} and \textit{N. Elezović}, J. Math. Inequal. 9, No. 4, 1181--1190 (2015; Zbl 1333.26034).
Yin, Li, Huang, Li-Guo, Lin, Xiu-Li
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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
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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
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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,
Yıldırım, Emrah, Ege, İncı
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Monotonicity, concavity, and inequalities related to the generalized digamma function
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 +3 more
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Monotonic and Logarithmically Convex Properties of a Function Involving Gamma Functions
Journal of Inequalities and Applications, 2009 Using the series-expansion of digamma functions and other techniques, some monotonicity and logarithmical concavity involving the ratio of gamma function are obtained, which is to give a partially affirmative answer to an open problem posed by B.-N.Guo ...
Tie-Hong Zhao +2 more
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