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A complete monotonicity property of the multiple gamma function [PDF]
Comptes Rendus. Mathématique, 2020 We consider the following functions \[ f_n(x)=1-\ln x+\frac{\ln G_n(x+1)}{x} \text{ and }g_n(x)=\frac{\@root x \of {G_n(x+1)}}{x},\; x\in (0,\infty ),\; n\in \mathbb{N}, \] where $G_n(z)=\left(\Gamma _n(z)\right)^{(-1)^{n-1}}$ and $\Gamma _n$ is the ...
Das, Sourav
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On criteria for algebraic independence of collections of functions satisfying algebraic difference relations [PDF]
Opuscula Mathematica, 2017 This paper gives conditions for algebraic independence of a collection of functions satisfying a certain kind of algebraic difference relations. As applications, we show algebraic independence of two collections of special functions: (1) Vignéras ...
Hiroshi Ogawara
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Frontiers in Systems Neuroscience, 2021 This article describes a neural model of the anatomy, neurophysiology, and functions of intrinsic and extrinsic theta rhythms in the brains of multiple species.
Stephen Grossberg
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Inequalities Involving $q$-Analogue of Multiple Psi Functions
Comptes Rendus. Mathématique, 2020 Logarithmic derivative of the multiple gamma function is known as the multiple psi function. In this work $q$-analogue of multiple psi functions of order $n$ have been considered.
Das, Sourav
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On a multiple Hilbert-type integral inequality involving the upper limit functions
Journal of Inequalities and Applications, 2021 By applying the weight functions, the idea of introducing parameters and the technique of real analysis, a new multiple Hilbert-type integral inequality involving the upper limit functions is given.
Jianhua Zhong, Bicheng Yang
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Scientific Reports, 2022 Working memory (WM) is a complex cognitive function involved in the temporary storage and manipulation of information, which has been one of the target cognitive functions to be restored in neurorehabilitation.
Jimin Park +3 more
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A Hardy–Hilbert-type integral inequality involving two multiple upper-limit functions
Journal of Inequalities and Applications, 2023 By means of the weight functions, the idea of introducing parameters and the technique of real analysis, a new Hardy–Hilbert-type integral inequality with the homogeneous kernel 1 ( x + y ) λ ( λ > 0 ) $\frac{1}{(x + y)^{\lambda}}\ (\lambda > 0 ...
Ricai Luo, Bicheng Yang, Leping He
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Neural Plasticity, 2021 Gamma oscillation (GAMMA) in the local field potential (LFP) is a synchronized activity commonly found in many brain regions, and it has been thought as a functional signature of network connectivity in the brain, which plays important roles in ...
Chuanliang Han +7 more
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Algorithms to Evaluate Multiple Sums for Loop Computations [PDF]
, 2013 We present algorithms to evaluate two types of multiple sums, which appear in higher-order loop computations. We consider expansions of a generalized hypergeometric-type sums, $\sum_{n_1,...,n_N} [Gamma(a1.n+c1) Gamma(a2.n}+c2) ...
Anzai, C., Sumino, Y.
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Massive-Scalar Effective Actions on Anti-de Sitter Spacetime [PDF]
, 1998 Closed forms are derived for the effective actions for free, massive spinless fields in anti-de Sitter spacetimes in arbitrary dimensions. The results have simple expressions in terms of elementary functions (for odd dimensions) or multiple Gamma ...
Burgess, C. P., Kamela, M.
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