Results 71 to 80 of about 5,444,686 (168)
Continued fractions and the polygamma functions
Journal of Computational and Applied Mathematics, 1983 AbstractIn a previous study we have shown that the polygamma functions (derivatives of the logarithm of the gamma function) relate to Stieltjes transforms in the square of the argument. These transforms in turn may be converted to Stieltjes continued fractions; in the background is a determined Stieltjes moment problem.In the present study we use the ...
Bowman, K.O., Shenton, L.R.
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Evaluation of Soil–Structure Interface Models Considering Cyclic Loading Effect
International Journal for Numerical and Analytical Methods in Geomechanics, Volume 48, Issue 17, Page 4257-4273, 10 December 2024.ABSTRACT The simulation of the soil–structure interface (SSI) under cyclic loading is critically important in geotechnical engineering. Numerous studies have been conducted to explore the cyclic behaviors exhibited at the SSI. However, existing model evaluations primarily rely on direct comparisons between experiments and simulations, with limited ...
Hai‐Lin Wang +3 more
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Families of specialized Euler sums [PDF]
Discrete Mathematics Letters, 2022 Anthony Sofo
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A note on additivity of polygamma functions
, 2009 In the note, the functions $\abs{ψ^{(i)}(e^x)}$ for $i\in\mathbb{N}$ are proved to be sub-additive on $(\lnθ_i,\infty)$ and super-additive on $(-\infty,\lnθ_i)$, where $θ_i\in(0,1)$ is the unique root of equation $2\abs{ψ^{(i)}(θ)}=\abs{ψ^{(i)}(θ^2)}$.
Qi, Feng, Guo, Bai-Ni
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Complete Monotonicity Properties of a Function Involving the Polygamma Function
Engineering and Applied Science Letters, 2018 In this paper, we study completete monotonicity properties of the function $f_{a,k}(x)=ψ^{(k)}(x+a) - ψ^{(k)}(x) - \frac{ak!}{x^{k+1}}$, where $a\in(0,1)$ and $k\in \mathbb{N}_0$. Specifically, we consider the cases for $k\in \{ 2n: n\in \mathbb{N}_0 \}$ and $k\in \{ 2n+1: n\in \mathbb{N}_0 \}$.
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On the Asymptotic Expansions of the (p,k)-Analogues of the Gamma Function and Associated Functions
AxiomsGeneral asymptotic expansion of the (p,k)-gamma function is obtained and various approaches to this expansion are studied. The numerical precision of the derived asymptotic formulas is shown and compared.
Tomislav Burić
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Closed-Form Solution for CFAR Detection Threshold in G0 Distributed SAR Clutter
IEEE AccessWe devise a constant false alarm rate (CFAR) detector for detecting targets in clutter regions with varying degrees of heterogeneity. The CFAR detector employs the $\mathcal {G}^{0}$ distribution for characterizing the statistics of background ...
Dheeren Ku Mahapatra +3 more
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Computing sums in terms of beta, polygamma, and Gauss hypergeometric functions
, 2023 In the paper, by virtue of the binomial inversion formula, a general formula of higher order derivatives for a ratio of two differentiable function, and other techniques, the authors compute several sums in terms of the beta function and its partial ...
Feng Qi (祁锋), Chuan-Jun Huang
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An inequality for the q-Polygamma function
Advanced Studies in Theoretical Physics, 2013 An Inequality for the q-Polygamma Function Banyat Sroysang Department of Mathematics and Statistics Faculty of Science and Technology Thammasat University, Pathumthani 12121 Thailand banyat@mathstat.sci.tu.ac.th Copyright c © 2013 Banyat Sroysang. This is an open access article distributed under the Creative Commons Attribution License, which permits ...
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Inequalities for Basic Special Functions Using Hölder Inequality
MathematicsLet p,q≥1 be two real numbers such that 1p+1q=1, and let a,b∈R be two parameters defined on the domain of a function, for example, f. Based on the well known Hölder inequality, we propose a generic inequality of the form |f(ap+bq)|≤|f(a)|1p|f(b)|1q, and ...
Mohammad Masjed-Jamei +2 more
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