Results 71 to 80 of about 5,395,506 (201)
Journal of Inequalities and Applications, 2020 Several conjectures posed by Qi on completely monotonic degrees of remainders for the asymptotic formulas of the digamma and trigamma functions are proved.
Ai-Min Xu, Zhong-Di Cen
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A certain family of infinite series associated with Digamma functions
Journal of Mathematical Analysis and Applications, 1991 The sums of several interesting infinite series were expressed recently in terms of the Psi (or Digamma) functions. The object of this paper is to present a systematic account of these (and of numerous similar or general) series whose sums can be found in the literature in various equivalent forms. Some relevant unifications and further generalizations
Al-Saqabi, B.N +2 more
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Semiclassical inequalities for Dirichlet and Neumann Laplacians on convex domains
Communications on Pure and Applied Mathematics, Volume 79, Issue 3, Page 762-822, March 2026.Abstract We are interested in inequalities that bound the Riesz means of the eigenvalues of the Dirichlet and Neumann Laplacians in terms of their semiclassical counterpart. We show that the classical inequalities of Berezin–Li–Yau and Kröger, valid for Riesz exponents γ≥1$\gamma \ge 1$, extend to certain values γ<1$\gamma <1$, provided the underlying ...
Rupert L. Frank, Simon Larson
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On an integral involving the logarithm function
, 2020 We use the Ramanujan's master theorem to evaluate the integral $$\int_{0}^{\infty}\frac{x^{l-1}}{(1+x)^{m+1}}\log^{n}(1+x)\, dx $$ in terms of the digamma function, the gamma function, and the Hurwitz zeta ...
Sumit Kumar Jha
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Journal of Inequalities and ApplicationsLet ψ ( x ) $\psi (x)$ denote the digamma function, that is, the logarithmic derivative of the classical Euler gamma function Γ ( x ) $\Gamma (x)$ . In the paper, the authors discover the monotonic properties of the functions ψ ( n ) ( x ) x ψ ( n + 1 ) (
Feng Qi, Dongkyu Lim, Kwara Nantomah
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, 2022 A modular relation of the form $F(\alpha, w)=F(\beta, iw)$, where $i=\sqrt{-1}$ and $\alpha\beta=1$, is obtained. It involves the generalized digamma function $\psi_w(a)$ which was recently studied by the authors in their work on developing the theory of
Kumar, Rahul +3 more
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Advanced Hermite-Hadamard-Mercer Type Inequalities with Refined Error Estimates and Applications
Fractal and FractionalThe purpose of this research is to develop a set of Hermite–Hadamard–Mercer-type inequalities that involve different types of fractional integral operators such as classical Riemann–Liouville fractional integral operators.
Arslan Munir +3 more
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Radio Number for Generalized Petersen Graphs
IEEE Access, 2019 Let $G$ be a connected graph and $d(\mu,\omega)$ be the distance between any two vertices of $G$ . The diameter of $G$ is denoted by $diam(G)$ and is equal to $\max \{d(\mu,\omega); \\ \mu,\omega \in G\}$ . The radio labeling (RL) for the graph
Feige Zhang +4 more
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Integrals Associated with the Digamma Integral Representation
, 2023 The definite integral with the kernel x/(x^2+b^2)/[\exp(2\pi x)-1] integrated from x=0 to infinity is the main term of a representation of the Digamma-Function psi(b), the derivative of the logarithm of the Gamma-Function. We present relations within the
Mathar, Richard J.
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