Results 51 to 60 of about 2,821,192 (174)
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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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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Some properties of the psi and polygamma functions
, 2009 In this paper, some monotonicity and concavity results of several functions involving the psi and polygamma functions are proved, and then some known inequalities are extended and generalized.
GUO, Bai-ni, Qİ, Feng
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Degenerate Analogues of Euler Zeta, Digamma, and Polygamma Functions [PDF]
Mathematical Problems in Engineering, 2020 In recent years, much attention has been paid to the role of degenerate versions of special functions and polynomials in mathematical physics and engineering. In the present paper, we introduce a degenerate Euler zeta function, a degenerate digamma function, and a degenerate polygamma function.
Fuli He +3 more
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Journal of Mathematics, Volume 2026, Issue 1, 2026.In this paper, we establish a unified approach of inequalities for the finite products (i · (i + k) · ⋅⋅(i + (n − 1)k))/(k · 2k · ⋅⋅(nk)), where k ≥ 2 is a fixed integer and i ∈ {1, 2, …, k − 1}. Motivated by previously known results for the cases k = 2, 3, 4, and 5, we express these products in terms of gamma function ratios and investigate the ...
Jenică Crînganu, Smritijit Sen
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SOME COMPLETELY MONOTONIC FUNCTIONS INVOLVING THE GAMMA AND POLYGAMMA FUNCTIONS [PDF]
Journal of the Korean Mathematical Society, 2008 Summary: Some logarithmically completely monotonic, strongly completely monotonic and completely monotonic functions related to the gamma, digamma and polygamma functions are established. Several inequalities, whose bounds are best possible, are obtained.
Li, Ai-Jun, Chen, Chao-Ping
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Fibonacci-Zeta infinite series associated with the polygamma functions
, 2022 We derive new infinite series involving Fibonacci numbers and Riemann zeta numbers. The calculations are facilitated by evaluating linear combinations of polygamma functions of the same order at certain ...
Kunle Adegoke, Sourangshu Ghosh
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Fractional Q$Q$‐curvature on the sphere and optimal partitions
Journal of the London Mathematical Society, Volume 112, Issue 6, December 2025.Abstract We study an optimal partition problem on the sphere, where the cost functional is associated with the fractional Q$Q$‐curvature in terms of the conformal fractional Laplacian on the sphere. By leveraging symmetries, we prove the existence of a symmetric minimal partition through a variational approach. A key ingredient in our analysis is a new
Héctor A. Chang‐Lara +2 more
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Estimation and Inference for Higher‐Order Stochastic Volatility Models With Leverage
Journal of Time Series Analysis, Volume 46, Issue 6, Page 1064-1084, November 2025.ABSTRACT Statistical inference—estimation and testing—for stochastic volatility models is challenging and computationally expensive. This problem is compounded when leverage effects are allowed. We propose efficient, simple estimators for higher‐order stochastic volatility models with leverage [SVL(p)$$ (p) $$], based on a small number of moment ...
Md. Nazmul Ahsan +2 more
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