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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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The multiple gamma function and its q-analogue [PDF]
Banach Center Publications, 1996 We give an asymptotic expansion (the higher Stirling formula) and an infinite product representation (the Weierstrass product formula) of the Vign\'{e}ras multiple gamma function by considering the classical limit of the multiple q-gamma function.Comment:
Nishizawa, Michitomo, Ueno, Kimio
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Aberrant hippocampal gamma oscillations in a mouse model of fragile X syndrome: insights from in vitro slice models [PDF]
Molecular AutismBackground Fragile X syndrome (FXS) is the most common inherited intellectual disability, caused by the loss of fragile X mental retardation protein (FMRP), which regulates neuronal signaling and plasticity.
Evangelia Pollali +7 more
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FL-GRM:Gamma Regression Algorithm Based on Federated Learning [PDF]
Jisuanji kexue, 2022 People commonly hypothesize that an independent variable follows a Gamma distribution in many areas,including hydrology,meteorology and insurance claim.Under the Gamma distribution assumption,Gamma regression model enables an outstanding fitting effect ...
GUO Yan-qing, LI Yu-hang, WANG Wan-wan, FU Hai-yan, WU Ming-kan, LI Yi
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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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The Multiple Gamma-Functions and the Log-Gamma Integrals [PDF]
International Journal of Mathematics and Mathematical Sciences, 2012 In this paper, which is a companion paper to [W], starting from the Euler integral which appears in a generalization of Jensen’s formula, we shall give a closed form for the integral of log . This enables us to locate the genesis of two new functions and considered by Srivastava and Choi. We consider the closely related functionA(a)and the Hurwitz zeta
X.-H. Wang, Y.-L. Lu
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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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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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Jackson's integral of multiple Hurwitz–Lerch zeta functions and multiple gamma functions [PDF]
Journal of Mathematical Analysis and Applications, 2018 Using the Jackson integral, we obtain the $q$-integral analogue of the Raabe type formulas for Barnes multiple Hurwitz-Lerch zeta functions and Barnes and Vardi's multiple gamma functions. Our results generalize $q$-integral analogue of the Raabe type formulas for the Hurwitz zeta functions and log gamma functions in [N. Kurokawa, K.
Su Hu, Daeyeoul Kim, Min-Soo Kim
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Frontiers in Psychiatry, 2020 BackgroundSchizophrenia patients exhibit cognitive deficits across multiple domains, including verbal memory, working memory, and executive function, which substantially contribute to psychosocial disability. Gamma oscillations are associated with a wide
Kumiko Tanaka-Koshiyama +12 more
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