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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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Associated Basic Hypergeometric Series [PDF]
Proceedings of the Glasgow Mathematical Association, 1953 The purpose of the present note is to give some interesting and simple identities connected with basic hypergeometric series of the types 2Φ1 and 3Φ2.
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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.
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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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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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GENERALIZED BASIC HYPERGEOMETRIC SERIES WITH UNCONNECTED BASES (II) [PDF]
The Quarterly Journal of Mathematics, 1967 In a series of recent papers Verma and Upadhyay (7,8,9) developed the theory of basic hypergeometric series with two bases q and q½. These investigations were made in an attempt to discover a summation formula for a bilateral basic hypergeometric series 2Ψ2 analogous to that for a 2H2 (cf.
Agarwal, R. P., Verma, A.
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Transformation formulas for multivariable basic hypergeometric series [PDF]
Methods and Applications of Analysis, 1999 We study multivariable (bilateral) basic hypergeometric series associated with (type $A$) Macdonald polynomials. We derive several transformation and summation properties for such series including analogues of Heine's ${}_2ϕ_1$ transformation, the $q$-Pfaff-Kummer and Euler transformations, the $q$-Saalschütz summation formula and Sear's transformation
Baker, T. H., Forrester, P. J.
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Gottlieb Polynomials and Their q-Extensions
Mathematics, 2021 Since Gottlieb introduced and investigated the so-called Gottlieb polynomials in 1938, which are discrete orthogonal polynomials, many researchers have investigated these polynomials from diverse angles.
Esra ErkuŞ-Duman, Junesang Choi
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Quadratic transformation formulas for basic hypergeometric series [PDF]
Transactions of the American Mathematical Society, 1993 Starting with some of the known transformation formulas for well-poised 2
Rahman, Mizan, Verma, Arun
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Fractal and Fractional, 2023 In the geometric function theory of complex analysis, the investigation of the geometric properties of analytic functions using q-analogues of differential and integral operators is an important area of study, offering powerful tools for applications in ...
Suha B. Al-Shaikh +3 more
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