Results 41 to 50 of about 5,444,686 (168)
A harmonic mean inequality for the polygamma function [PDF]
Mathematical Inequalities & Applications, 2020 Summary: In this work, we discuss some new inequalities and a concavity property of the poly-gamma function \(\psi^{(n)}(x) =\frac{d^n}{dx^n} \psi(x)\), \(x>0\), where \(\psi(x)\) represents the digamma function (i.e., logarithmic derivative of the gamma function \(\Gamma(x)\)). Using these inequalities, the minimum value of the harmonic mean of \((-1)^
Das, Sourav, Swaminathan, A.
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Pole decomposition of BFKL eigenvalue at zero conformal spin and the real part of digamma function
Physics Letters BWe 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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Accurate approximations to the polygamma functions [PDF]
Quarterly of Applied Mathematics, 1979 Empirically obtained approximations to the polygamma functions ψ
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ON FUNCTIONAL INEQUALITIES FOR THE PSI FUNCTION
Проблемы анализаMotivated by the works of Bougotta and Mercer, the authors in this paper study the monotonicity of the function x↦ψ(1+bx)^a/ψ(1+ax)^b, and establish several inequalities involving the psi function.
Barkat A. Bhayo +2 more
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Abstract and Applied Analysis, Volume 2026, Issue 1, 2026.In this paper, we introduce a new two‐parameter deformation of the gamma function that generalizes some existing gamma‐type functions in the literature. We study properties of this function that depend on the parameters. We also prove some inequalities for the corresponding beta function and polygamma functions.
Anton Asare-Tuah +5 more
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Harmonic series with polygamma functions [PDF]
Journal of Classical Analysis, 2016 Summary: The paper is about evaluating in closed form the following classes of series involving the product of the \(n\)th harmonic number and the polygamma functions \[ \begin{aligned} S_k &= \sum_{n=1}^\infty H_n\left(\zeta(k)-1-\frac{1}{s^k}-\dots -\frac {1}{n^k}\right)=\frac{(-1)^k}{(k-1)!}\sum_{n=1}^\infty H_n\varPsi^{(k-1)}(n+1),\quad k\geqslant ...
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Advances in High Energy Physics, Volume 2026, Issue 1, 2026.In this paper, we presented an approximate analytical treatment of the Coulomb plus logarithmic potential using time‐independent perturbation theory to investigate the mass spectra of bottomonium and charmonium mesons for the low‐order quantum states.
E. Omugbe +4 more
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On complete monotonicity for several classes of functions related to ratios of gamma functions
Journal of Inequalities and Applications, 2019 Let Γ(x) $\varGamma (x)$ denote the classical Euler gamma function. The logarithmic derivative ψ(x)=[lnΓ(x)]′=Γ′(x)Γ(x) $\psi (x)=[\ln \varGamma (x)]'=\frac{\varGamma '(x)}{ \varGamma (x)}$, ψ′(x) $\psi '(x)$, and ψ″(x) $\psi ''(x)$ are, respectively ...
Feng Qi, Ravi P. Agarwal
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Beyond the Tail: Taming Bias in Burr XII Residual Entropy Estimation
International Journal of Mathematics and Mathematical Sciences, Volume 2026, Issue 1, 2026.Accurately predicting system lifetime is routine in reliability and survival analysis, but quantifying uncertainty in residual life is rarely addressed despite being often more critical. Residual entropy fills this gap by measuring unpredictability in remaining lifetime.
Amal Helu +4 more
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Monotonicity of a mean related to polygamma functions with an application
Journal of Inequalities and Applications, 2016 Let ψ n = ( − 1 ) n − 1 $\psi_{n}= ( -1 ) ^{n-1}$ ψ ( n ) $\psi^{ ( n ) }$ ( n = 0 , 1 , 2 , … $n=0,1,2,\ldots $ ), where ψ ( n ) $\psi^{ ( n ) }$ denotes the psi and polygamma functions.
Zhen-Hang Yang, Shen-Zhou Zheng
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