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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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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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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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Special values of multiple gamma functions [PDF]
Journal de théorie des nombres de Bordeaux, 2008 We give a Chowla-Selberg type formula that connects a generalization of the eta-function to GL(n) with multiple gamma functions. We also present some simple infinite product identities for certain special values of the multiple gamma function.
Duke, William, Imamoḡlu, Özlem
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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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Multiple Gamma functions and $L$-functions [PDF]
Mathematical Research Letters, 1996 Multiple gamma functions, first introduced and studied by E. W. Barnes and others around 1900, play an important role in the study of functional equations for Selberg zeta functions and other topics in modern analytic number theory. This paper makes a case for defining a multiple gamma function as a meromorphic function \(\Gamma_P(u)\) associated with ...
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Multiple $$\log \Gamma $$ -Type Functions
, 2022 AbstractIn this chapter, we introduce and investigate the map, denote it by Σ, that carries any function g lying in $$\displaystyle \bigcup _{p\geq 0}(\mathcal {D}^p\cap \mathcal {K}^p) $$ ⋃ p ≥ 0
Jean-Luc Marichal, Naïm Zenaïdi
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Bounds for triple gamma functions and their ratios
Journal of Inequalities and Applications, 2016 In this work, in addition to the bounds for triple gamma function, bounds for the ratios of triple gamma functions are obtained. Similar bounds for the ratios of the double gamma functions are also obtained.
Sourav Das, A Swaminathan
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