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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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 [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
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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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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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Extension of complete monotonicity results involving the digamma function
Moroccan Journal of Pure and Applied Analysis, 2018 By using some analytical techniques, we prove a complete monotonicity property of a certain function involving the (p, k)-digamma function. Subsequently, we derive some inequalities for the (p, k)- digamma function.
Nantomah Kwara
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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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The sum of the series of reciprocals of the cubic polynomials with one zero and double non-zero integer root [PDF]
Mathematics in Education, Research and Applications, 2019 This contribution is a follow-up to author’s previous published papers and deals with the sum of the series of reciprocals of the cubic polynomials with one zero and double non-zero integer root.
Radovan Potůček
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MONOTONICITY AND CONVEXITY PROPERTIES OF THE NIELSEN’S β-FUNCTION
Проблемы анализа, 2017 The Nielsen’s β-function provides a powerful tool for evaluating and estimating certain integrals, series and mathematical constants. It is related to other special functions such as the digamma function, the Euler’s beta function and the Gauss ...
Kwara Nantomah
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Complete monotonicity related to the k-polygamma functions with applications
Advances in Difference Equations, 2019 In this paper, we prove complete monotonicity of some functions involving k-polygamma functions. As an application of the main result, we also give new upper and lower bounds of the k-digamma function.
Li Yin, Jumei Zhang, XiuLi Lin
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