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Transformations and summations for bilateral basic hypergeometric series
We derive transformation and summation formulas for bilateral basic hypergeometric series. As a starting point, we use two transformations of bilateral basic very-well-poised ${}_8Ψ_8$. The first transformation is given as a sum of two nonterminating ${}_8W_7$'s and the second is given in terms of a sum of a ${}_4ψ_4$ and two balanced ${}_4ϕ_3$'s. From
Cohl, Howard S., Schlosser, Michael J.
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Single‐Cell Insights Into Cellular Response in Abdominal Aortic Occlusion‐Induced Hippocampal Injury
CNS Neuroscience &Therapeutics, Volume 31, Issue 1, January 2025.In this study, single‐cell RNA sequencing (scRNA‐seq) was used to analyze the cellular response in the hippocampus of a mouse model with abdominal aortic occlusion (AAO) injury. We identified changes in cell proportion, including astrocytes and oligodendrocyte precursor cells (OPCs), and observed gene expression changes associated with neurogenesis and
Changhong Ren +10 more
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Advanced Science, Volume 11, Issue 23, June 19, 2024.This study reveals how collagen/nanohydroxyapatite‐based bone repair materials regulate the osteoimmune microenvironment via combining single‐cell RNA sequencing and spatial transcriptomics analyses. The Mgp high‐expressing MSCs with efficient osteogenic differentiation potential are found to be aggregated around implanted materials at the early stage ...
Zhuqing Wan +13 more
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Mock Theta Function Identities Deriving from Bilateral Basic Hypergeometric Series [PDF]
, 2017 The bilateral series corresponding to many of the third-, fifth-, sixth- and eighth order mock theta functions may be derived as special cases of $_2 _2$ series \[ \sum_{n=-\infty}^{\infty}\frac{(a,c;q)_n}{(b,d;q)_n}z^n. \] Three transformation formulae for this series due to Bailey are used to derive various transformation and summation formulae for ...
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Resonance of Continued Fractions Related to2ψ2Basic Bilateral Hypergeometric Series [PDF]
Kyungpook mathematical journal, 2011 Summary: In this paper, making use of transformation due to \textit{S. N. Singh} [Proc. Natl. Acad. Sci. India, Sect. A 65, No.3, 319--329 (1995; Zbl 0992.33501)], an attempt has been made to establish certain results involving basic bilateral hypergeometric series and continued fractions.
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Molecular Oncology, Volume 19, Issue S1, Page 1-940, June 2025.Abstracts submitted to the ‘EACR 2025 Congress: Innovative Cancer Science’, from 16–19 June 2025 and accepted by the Congress Organising Committee are published in this Supplement of Molecular Oncology, an affiliated journal of the European Association for Cancer Research (EACR).
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Summation formulae for the bilateral basic hypergeometric series ${}_1��_1 ( a; b; q, z )$
, 2016 17 ...
Mori, Hironori, Morita, Takeshi
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On a ${\mathbb C}^2$-valued integral index transform and bilateral hypergeometric series
, 2021 We discuss the spectral decomposition of the hypergeometric differential operators on the line $\mathrm{Re}\, z=1/2$. Such operators arise in the problem of decomposition of tensor products of unitary representations of the universal covering of the group $SL(2\,{\mathbb R}$.
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An asymptotic formula of the divergent bilateral basic hypergeometric series
, 2012 We show an asymptotic formula of the divergent bilateral basic hypergeometric series ${}_1 _0 (a;-;q,\cdot)$ with using the $q$-Borel-Laplace method. We also give the limit $q\to 1-0$ of our asymptotic formula.
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A NOTE ON TRANSFORMATION FORMULAE FOR BILATERAL BASIC HYPERGEOMETRIC SERIES [PDF]
International Journal of Apllied Mathematics, 2013 Srivastava, Pankaj +3 more
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