On transformation of certain bilateral basic hypergeometric series and their applications
Proceedings - Mathematical Sciences, 2019 In this paper, the authors presented transformation and summation formulae for bilateral basic hypergeometric series: \[\sum_{n=-\infty}^{\infty}\frac{(a)_n}{(b)_n}z^n= \frac{(b/a;q)_\infty}{(b,bz/a;q)_\infty}\sum_{n=-\infty}^{\infty}(a)_nz^n\] whenever \(\max\{|b/a|,|1/b|\}
D. D. Somashekara, K. N. Vidya
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Bilateral Basic Hypergeometric Series
, 2004 Wenchang Chu, Di Claudio Leontina
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Motor performance and higher associative cortical networks in adolescents with neonatal hypoxic-ischaemic encephalopathy treated with therapeutic hypothermia. [PDF]
Dev Med Child NeurolSeveral functional connections between ROIs in the somatomotor (purple) and the default mode network (gray) were significantly associated with the MABC‐2 “aiming and catching” sub‐domain in the HIE cohort in comparison to controls. The colors of the connections represents the correlation coefficient with either negative (light blue to magenta) or ...
Håkansson G +5 more
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Four Variants of Riemann Zeta Function
Mathematics, 2022 By means of the generating function method and Dougall’s formulae for bilateral hypergeometric series, we examine four classes of infinite series, which may be considered as variants of Riemann zeta function. Several summation formulae are established in
Nadia N. Li, Wenchang Chu
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BPS indices, modularity and perturbations in quantum K-theory
Journal of High Energy Physics, 2022 We study a perturbation family of N $$ \mathcal{N} $$ = 2 3d gauge theories and its relation to quantum K-theory. A 3d version of the Intriligator-Vafa formula is given for the quantum K-theory ring of Grassmannians.
Hans Jockers +3 more
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State-specific Regulation of Electrical Stimulation in the Intralaminar Thalamus of Macaque Monkeys: Network and Transcriptional Insights into Arousal. [PDF]
Adv Sci (Weinh)This study identifies an ILN‐driven arousal network responsible for rapid arousal during anesthesia through simultaneous EEG‐fMRI and DBS in macaques. Network‐based RNA sequencing reveals genes preferentially expressed within this arousal network, notably enriched in potassium channels and excitatory, parvalbumin‐expressing neurons, and ...
Zhang Z +9 more
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Hypergeometric Solutions of the $A_4^{(1)}$-Surface $q$-Painlev\'e IV Equation [PDF]
, 2014 We consider a $q$-Painlev\'e IV equation which is the $A_4^{(1)}$-surface type in the Sakai's classification. We find three distinct types of classical solutions with determinantal structures whose elements are basic hypergeometric functions. Two of them
Nakazono, Nobutaka
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New Curious Bilateral q-Series Identities
Axioms, 2012 By applying a classical method, already employed by Cauchy, to a terminating curious summation by one of the authors, a new curious bilateral q-series identity is derived.
Frédéric Jouhet, Michael J. Schlosser
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On generalization of continued fraction of Gauss
International Journal of Mathematics and Mathematical Sciences, 1990 In this paper we establish a continued fraction represetation for the ratio qf two basic bilateral hypergeometric series 2ψ2's which generalize Gauss' continued fraction for the ratio of two 2F1's.
Remy Y. Denis
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Basic Hypergeometric Functions as Limits of Elliptic Hypergeometric Functions [PDF]
, 2009 We describe a uniform way of obtaining basic hypergeometric functions as limits of the elliptic beta integral. This description gives rise to the construction of a polytope with a different basic hypergeometric function attached to each face of this ...
Rains, Eric M., van de Bult, Fokko J.
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