Results 11 to 20 of about 6,972,539 (190)
Macdonald Polynomials and Multivariable Basic Hypergeometric Series [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2007 We study Macdonald polynomials from a basic hypergeometric series point of view. In particular, we show that the Pieri formula for Macdonald polynomials and its recently discovered inverse, a recursion formula for Macdonald polynomials, both represent ...
Michael J. Schlosser
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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 ApplicationsThe 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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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
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Some transformations of basic hypergeometric series and their applications [PDF]
Proceedings of the American Mathematical Society, 1980 Using Baileyโs 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
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International Journal of Mathematics and Mathematical Sciences, 2011 We have obtained a new summation formula for 2๐2 bilateral basic hypergeometric series by the method of parameter augmentation and demonstrated its various uses leading to some development of etafunctions, ๐-gamma, and ๐-beta function identities.
D. D. Somashekara +2 more
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Applications of ๐-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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Transformations and Summations for Bilateral Basic Hypergeometric Series. [PDF]
Arab J MathAbstract We review and derive transformation and summation formulas for bilateral basic hypergeometric series. Our study focuses on consequences of certain bilateral extensions of two important results by Bailey, namely a transformation for very-well-poised
Cohl HS, Schlosser MJ.
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A remarkable basic hypergeometric identity. [PDF]
Ramanujan JWe give a closed form for $quotients$ of truncated basic hypergeometric series where the base $q$ is evaluated at roots of unity.Comment: $1+2+\dots+N = 1\cdot2\dotsb N ...
Krattenthaler C, Zudilin W.
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Cyclotomic valuation of q-Pochhammer symbols and q-integrality of basic hypergeometric series [PDF]
, 2022 We give a formula for the cyclotomic valuation of $q$-Pochhammer symbols in terms of (generalized) Dwork maps. We also obtain a criterion for the $q$-integrality of basic hypergeometric series in terms of certain step functions, which generalize Christol
Bell, J. P. +8 more
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