Results 21 to 30 of about 1,384 (130)

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
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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
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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

On the equivalence of two fundamental theta identities [PDF]

, 2014
Two fundamental theta identities, a three-term identity due to Weierstrass and a five-term identity due to Jacobi, both with products of four theta functions as terms, are shown to be equivalent.
Koornwinder, Tom H.
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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
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Limits of elliptic hypergeometric biorthogonal functions [PDF]

, 2011
The purpose of this article is to bring structure to (basic) hypergeometric biorthogonal systems, in particular to the q-Askey scheme of basic hypergeometric orthogonal polynomials.
Askey, Atakishiyev, Eric M. Rains, Fokko J. van de Bult, Gasper, Koekoek, Macdonald, Pastro, Rains, Rains, Rosengren, Spiridonov, Spiridonov, Spiridonov, Spiridonov, van de Bult   +15 more
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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

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.
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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
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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
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