Results 21 to 30 of about 2,042 (145)

Properties of generalized univariate hypergeometric functions [PDF]

, 2006
Based on Spiridonov's analysis of elliptic generalizations of the Gauss hypergeometric function, we develop a common framework for 7-parameter families of generalized elliptic, hyperbolic and trigonometric univariate hypergeometric functions.
B. Nassrallah, D.P. Gupta, E. Koelink, E. Koelink, E. Koelink, E. M. Rains, F. J. van de Bult, F.J. Bult van de, G. Gasper, G. Letzter, J. V. Stokman, J.F. Diejen van, J.V. Stokman, J.V. Stokman, M. Noumi, M. Put van der, M. Rahman, M.E.H. Ismail, S. Lievens, S.N.M. Ruijsenaars, S.N.M. Ruijsenaars, S.N.M. Ruijsenaars, S.N.M. Ruijsenaars, T. Shintani, V.P. Spiridonov, V.P. Spiridonov, W. Groenevelt, Y. Komori   +27 more
core   +4 more sources

A new multivariable 6-psi-6 summation formula [PDF]

, 2006
By multidimensional matrix inversion, combined with an A_r extension of Jackson's 8-phi-7 summation formula by Milne, a new multivariable 8-phi-7 summation is derived.
C. Krattenthaler, C. Krattenthaler, D.M. Bressoud, E.M. Rains, F.H. Jackson, G. Bhatnagar, G. Gasper, G.E. Andrews, G.E. Andrews, G.M. Lilly, H. Coskun, H. Rosengren, I.B. Frenkel, J.F. Diejen van, M. Ito, M. Ito, M. Lassalle, M. Schlosser, M. Schlosser, M. Schlosser, M.E.H. Ismail, Michael Schlosser, R. Askey, R.A. Gustafson, R.A. Gustafson, S.C. Milne, S.C. Milne, S.C. Milne, S.C. Milne, T.J., l’A Bromwich, W.J. Holman III, W.N. Bailey   +31 more
core   +1 more source

A Bilateral Series Involving Basic Hypergeometric Functions [PDF]

, 2005
We prove a summation formula for a bilateral series whose terms are products of two basic hypergeometric functions. In special cases, series of this type arise as matrix elements of quantum group representations.
openaire   +2 more sources

Radial limits of mock theta functions [PDF]

, 2014
Inspired by the original definition of mock theta functions by Ramanujan, a number of authors have considered the question of explicitly determining their behavior at the cusps.
Bringmann, Kathrin, Rolen, Larry
core   +2 more sources

A simple proof of Bailey's very-well-poised 6-psi-6 summation

, 2000
We give elementary derivations of some classical summation formulae for bilateral (basic) hypergeometric series. In particular, we apply Gauss' 2-F-1 summation and elementary series manipulations to give a simple proof of Dougall's 2-H-2 summation ...
Schlosser, M.
core   +1 more source

A new A_n extension of Ramanujan's 1-psi-1 summation with applications to multilateral A_n series

, 2000
In this article, we derive some identities for multilateral basic hypergeometric series associated to the root system A_n. First, we apply Ismail's argument to an A_n q-binomial theorem of Milne and derive a new A_n generalization of Ramanujan's 1-psi-1 ...
Milne, S. C., Schlosser, M.
core   +1 more source

New Mock Theta Function Identities via Fractional q-Calculus and Bilateral ₂ψ₂ Series

Fractal and Fractional
Mock theta functions, introduced by Ramanujan in his last letter to Hardy, play a significant role in q-series theory and have natural connections to fractional q-calculus. In this paper, we study bilateral hypergeometric series of the form ψ22= ∑n=−∞∞(a,
Qiuxia Hu, Bilal Khan
doaj   +1 more source

Multilateral inversion of A_r, C_r and D_r basic hypergeometric series

, 2006
In [Electron. J. Combin. 10 (2003), #R10], the author presented a new basic hypergeometric matrix inverse with applications to bilateral basic hypergeometric series.
D.M. Bressoud, F.H. Jackson, G. Bhatnagar, G. Bhatnagar, G. Bhatnagar, G. Gasper, G.M. Lilly, H. Rosengren, I.B. Frenkel, M. Jackson, M.J. Schlosser, M.J. Schlosser, M.J. Schlosser, Michael J. Schlosser, R.A. Gustafson, R.A. Gustafson, R.Y. Denis, S.C. Milne, S.C. Milne, S.C. Milne, S.C. Milne, W.J. Holman III, W.N. Bailey   +22 more
core   +1 more source

Microglial GPR35 Ameliorates Epileptogenesis and Neuroinflammation via PDGFA Domain 2 Signaling

Advanced Science, Volume 13, Issue 19, 2 April 2026.
Activation of microglial G protein–coupled receptor 35 (GPR35) by L‐kynurenic acid (L‐Kyna) initiates a platelet‐derived growth factor A (PDGFA)–dependent phosphoinositide 3‐kinase–protein kinase B (PI3K–AKT) signaling cascade that dampens hippocampal neuroinflammation, thereby restraining epileptogenesis, lowering seizure susceptibility, and ...
Qi Wang, Tingting Qu, Qibing Sun, Ran Li, Junfei Dong, Yuming Du, Ziyin Xuan, Lei Wang, Hanli Li, Jianyun Sun, Fangliang Chen, Jinshuai Liu, Zifan Yang, Jianxiang Lei, Qian Yang, Bin Wang, Zhiming Zhou, Yu Wang   +17 more
wiley   +1 more source

Several transformation formulas involving bilateral basic hypergeometric series

, 2019
In terms of the analytic continuation method, we prove three transformation formulas involving bilateral basic hypergeometric series. One of them is equivalent to Jouhet's result involving two $_8 _8$ series and two $_8 _7$ series.
Wei, Chuanan, Yu, Tong
openaire   +2 more sources