Results 11 to 20 of about 2,042 (145)

Bilateral inversions and terminating basic hypergeometric series identities

Discrete Mathematics, 2009
A \(q\)-analogue of the Legendre inversion is established and generalized to bilateral sequences. They are employed to investigate the dual relations of three basic formulae due to Jackson and Bailey, on balanced \(_{3}\phi_{2}\)-series, well-poised \(_{8}\phi_{7}\)-series and bilateral \(_{6}\psi_{6}\)-series.
CHU, Wenchang, WANG C.
openaire   +5 more sources

On certain transformations of poly-basic bilateral hypergeometric series

Journal of Computational and Applied Mathematics, 2003
The authors establish transformations of poly-basic bilateral hypergeometric series in terms of another similar series not necessary having the same number of bases. As application of the obtained results, they derive expressions of the product of two \(q\)-series in terms of another product of two series which lead to interesting transformations of ...
Denis, Remy Y., Singh, S.N., Singh, S.P.
openaire   +4 more sources

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|\}
Somashekara, D. D., Vidya, K. N.
openaire   +3 more sources

Motor performance and higher associative cortical networks in adolescents with neonatal hypoxic-ischaemic encephalopathy treated with therapeutic hypothermia. [PDF]

Dev Med Child Neurol
Several 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, Eriksson Westblad M, Örtqvist M, Ådén U, Blennow M, Fransson P.   +5 more
europepmc   +2 more sources

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
doaj   +1 more source

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
doaj   +1 more source

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, Huang Y, Chen X, Li J, Yang Y, Lv L, Wang J, Wang M, Wang Y, Wang Z.   +9 more
europepmc   +2 more sources

ON BILATERAL BASIC HYPERGEOMETRIC SERIES AND CONTINUED FRACTIONS

International Journal of Apllied Mathematics, 2013
Summary: This article deals with the derivation of continued fraction involving bilateral basic hypergeometric series by making use of known three term relations and other known results of R. P. Agarwal.
Srivastava, Pankaj, Mishra, Devendra Kumar   +1 more
openaire   +2 more sources

On a New Summation Formula for 𝟐𝜓𝟐 Basic Bilateral Hypergeometric Series and Its Applications

International Journal of Mathematics and Mathematical Sciences, 2011
We have obtained a new summation formula for 2𝜓2 bilateral basic hypergeometric series by the method of parameter augmentation and demonstrated its various uses leading to some development of etafunctions, 𝑞-gamma, and 𝑞-beta function identities.
D. D. Somashekara, K. Narasimha Murthy, S. L. Shalini   +2 more
doaj   +1 more source

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.
core   +5 more sources