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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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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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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Pole decomposition of BFKL eigenvalue at zero conformal spin and the real part of digamma function
Physics Letters B, 2023 We consider the powers of leading order eigenvalue of the Balitsky-Fadin-Kuraev-Lipatov (BFKL) equation at zero conformal spin. Using reflection identities of harmonic sums we demonstrate how involved generalized polygamma functions are introduced by ...
Mohammad Joubat +2 more
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A Rational Approximant for the Digamma Function [PDF]
Numerical Algorithms, 2003 Power series representations for special functions are computationally satisfactory only in the vicinity of the expansion point. Thus, it is an obvious idea to use instead Padé approximants or other rational functions constructed from sequence transformations.
Ernst Joachim Weniger
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On the positivity of a certain function related with the Digamma function [PDF]
The Ramanujan Journal, 2023 Abstract In this note, we prove that $$\begin{aligned} \left( \frac{x^n}{1-e^{-x}}\right) ^{(n)}>0 \end{aligned}$$
K. Castillo
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Monotonicity, concavity, and inequalities related to the generalized digamma function [PDF]
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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Best Approximation for the k-digamma Functions
Asian Research Journal of Mathematics, 2019 In this paper, we show a best approximation for the k-digamma functions.
Junbo Zhao, Li Yin, Xinxin Deng
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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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New Approximation Formula of Digamma Function with Bounded Remainder [PDF]
MathematicsThis study establishes the new approximation formula for the Digamma function ψ(s)=lns−12s−112ss2+θ(s ...
Mansour Mahmoud +2 more
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