Results 11 to 20 of about 5,521 (197)

Inversion of Bilateral Basic Hypergeometric Series [PDF]

The Electronic Journal of Combinatorics, 2003
We present a new matrix inverse with applications in the theory of bilateral basic hypergeometric series. Our matrix inversion result is directly extracted from an instance of Bailey's very-well-poised ${}_6\psi_6$ summation theorem, and involves two infinite matrices which are not lower-triangular.
Michael Schlosser
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Factorization of Basic Hypergeometric Series

Symmetry, Integrability and Geometry: Methods and Applications
The general problem of the factorization of a basic hypergeometric series is presented and discussed. The case of the general $_2\psi_2$ series is examined in detail. Connections are found with the theory of basic hypergeometric series on root systems. Alternative proofs of several well-known summation and transformation formulae, including Gustafson's
Bradley-Thrush, Jonathan G.
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The Cauchy operator for basic hypergeometric series

Advances in Applied Mathematics, 2008
We introduce the Cauchy augmentation operator for basic hypergeometric series. Heine's ${}_2ϕ_1$ transformation formula and Sears' ${}_3ϕ_2$ transformation formula can be easily obtained by the symmetric property of some parameters in operator identities.
Vincent Y. B. Chen, Nancy S. S. Gu
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Particle seas and basic hypergeometric series

Advances in Applied Mathematics, 2003
A particle sea is a geometrical arrangement in the upper half plane, of two types of symbols, say squares and circles, subject to some conditions. Loosely speaking, particle seas are in some sense an analogue of Ferrers graphs from the theory of partitions.
Corteel, Sylvie
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Some transformations of basic hypergeometric series and their applications [PDF]

Proceedings of the American Mathematical Society, 1980
Using Bailey’s transformation, relations between basic and basic bilateral hypergeometric series are obtained. Some interesting special cases, like identities of Rogers-Ramanujan type, summation theorems for particular basic bilateral hypergeometric series
V. K. Jain
openaire   +2 more sources

On Convergence of q-Series Involving ϕr+1r Basic Hypergeometric Series

Journal of Inequalities and Applications, 2009
We use inequality technique and the terminating case of the q-binomial formula to give some results on convergence of q-series involving ϕr+1r basic hypergeometric series.
Mingjin Wang, Xilai Zhao
doaj   +2 more sources

Parameter Augmentation for Basic Hypergeometric Series, I

Journal of Combinatorial Theory, Series A, 1997
[For part I see the authors in Prog. Math. 161, 111--129 (1998; Zbl 0901.33008).] Let \(D_q\) be the \(q\)-difference operator, \( D_qf(a) = (f(a) - f(aq))/a\), and define an exponential operator \(T\) by \[ T(bD_q) = \sum_{n=0}^{\infty} {(bD_q)^n \over (q;q)_n}. \] The authors derive many known results by applying this operator to simpler results.
William Y. C. Chen, Zhi-Guo Liu
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Applications of 𝑞-Lagrange inversion to basic hypergeometric series [PDF]

Transactions of the American Mathematical Society, 1983
A family of q q -Lagrange inversion formulas is given.
Gessel, Ira, Stanton, Dennis
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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
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Abel's lemma on summation by parts and basic hypergeometric series

Advances in Applied Mathematics, 2007
The author continues to explore the use of Abel's lemma on summation by parts to prove basic hyperegeometric series identities. He gives simple proofs of unilateral and bilateral series identities such as the \(q\)-binomial theorem, the \(_1\psi_1\) summation [transcribed from Aequationes Math. 72, No.
Chu, Wenchang
openaire   +4 more sources