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Human Brain Mapping, Volume 43, Issue 4, Page 1231-1255, March 2022., 2022 The electroencephalography–functional magnetic resonance imaging fusion methods that have been reported so far ignore the underlying multi‐way nature of the data in at least one of the modalities and/or rely on very strong assumptions concerning the relation of the respective datasets.
Christos Chatzichristos +5 more
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A class of completely monotonic functions involving the polygamma functions
Journal of Inequalities and Applications, 2022 Let Γ ( x ) $\Gamma (x)$ denote the classical Euler gamma function. We set ψ n ( x ) = ( − 1 ) n − 1 ψ ( n ) ( x ) $\psi _{n}(x)=(-1)^{n-1}\psi ^{(n)}(x)$ ( n ∈ N $n\in \mathbb{N}$ ), where ψ ( n ) ( x ) $\psi ^{(n)}(x)$ denotes the nth derivative of the
Li-Chun Liang, Li-Fei Zheng, Aying Wan
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Geometric Flow Equations for the Number of Space‐Time Dimensions
Fortschritte der Physik, Volume 70, Issue 1, January 2022., 2022 Abstract In this paper we consider new geometric flow equations, called D‐flow, which describe the variation of space‐time geometries under the change of the number of dimensions. The D‐flow is originating from the non‐trivial dependence of the volume of space‐time manifolds on the number of space‐time dimensions and it is driven by certain curvature ...
Davide De Biasio +2 more
wiley +1 more source
A functional inequality for the polygamma functions [PDF]
Bulletin of the Australian Mathematical Society, 2005 Let where ψ denotes the logarithmic derivative of Euler's gamma function. We prove that the functional inequalityholds if and only if 0 < r ≤ 1. And, we show that the converse is valid if and only if r < 0 or r ≥ n + 1.
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A procedure for generating infinite series identities
International Journal of Mathematics and Mathematical Sciences, 2004 A procedure for generating infinite series identities makes use of the generalized method of exhaustion by analytically evaluating the inner series of the resulting double summation.
Anthony A. Ruffa
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Monotonicity results for the polygamma functions [PDF]
Mathematical Inequalities & Applications, 2008 The psi(or digamma) function is defined for all positive real numbers \(x\) as the logarithmic derivative of the gamma function \(\psi(x)=\frac{\Gamma'(x)}{\Gamma(x)}.\) Its derivatives \(\psi^{(n)}(x)\) are called polygamma functions. In the paper under review, the authors investigate monotonicity of the functions \[ x^c| \psi^{(n)}(x+\beta)| , \qquad
Li, Ai-Jun, Yuan, Jun, Chen, Chao-Ping
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Refinements of Some Recent Inequalities for Certain Special Functions
Annales Mathematicae Silesianae, 2019 The aim of this paper is to give some refinements to several inequalities, recently etablished, by P.K. Bhandari and S.K. Bissu in [Inequalities via Hölder’s inequality, Scholars Journal of Research in Mathematics and Computer Science, 2 (2018), no.
Akkouchi Mohamed +1 more
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Tur\'an-type inequaities for generalized polygamma function [PDF]
, 2022 Inspired by the work of C. Mortici [1] and A. Laforgia et. al [2] we have established some new Tur\'an-type inequalities for k-polygamma function and p-k-polygamma function.Comment: 6 ...
Atale, Omprakash
core
Short Remarks on Complete Monotonicity of Some Functions
Mathematics, 2020 In this paper, we show that the functions x m | β ( m ) ( x ) | are not completely monotonic on ( 0 , ∞ ) for all m ∈ N , where β ( x ) is the Nielsen’s β -function and we prove the functions x m − 1
Ladislav Matejíčka
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Tokyo Journal of Mathematics, 2007 The author studies the Polygamma Functions defined by \[ \psi_n(\omega)=\frac{d^{n+1}}{d\omega^{n+1}}\left[ \ln \Gamma (\omega) \right], \] where \((n+\omega)\notin O_2,\) \(m\in N\cup\{ 0 \}, \) \(n\in N\) and \(O_2\) is the set of non-invertible elements in \(C_2=\{ a+bi_1 +ci_2 +di_1i_2: \, i_1^2=i_2^2=-1,\, a,b,c,d \in R \},\) \(\Gamma(\omega)\) --
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