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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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Inversion of bilateral basic hypergeometric series [PDF]
The Electronic Journal of Combinatorics, 2002 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 J. Schlosser
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$q$-Supercongruences from squares of basic hypergeometric series [PDF]
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2021 We give some new $q$-supercongruences on truncated forms of squares of basic hypergeometric series. Most of them are modulo the cube of a cyclotomic polynomial, and two of them are modulo the fourth power of a cyclotomic polynomial. The main ingredients of our proofs are the creative microscoping method, a lemma of El Bachraoui, and the Chinese ...
Victor J. W. Guo, Long Li
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Bijective proofs of basic hypergeometric series identities [PDF]
Pacific Journal of Mathematics, 1987 The authors give simple, completely bijective proofs of the \(q\)-binomial theorem and Heine's \({}_2\Phi_1\) transformation. Since all identities on basic hypergeometric series can be built out of these two fundamental identities, any basic hypergeometric identity can be proved bijectively, at least in theory, by building bijections out of these ...
J. T. Joichi, Dennis Stanton
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Lattice paths and multiple basic hypergeometric series [PDF]
Pacific Journal of Mathematics, 1989 The equivalence between certain identities for basic hypergeometric series and some combinatorial identities for colored partitions is established by viewing the basic hypergeometric series as generating functions for weighted lattice paths.
Ashok Agarwal, David M. Bressoud
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RESULTS ON BASIC HYPERGEOMETRIC SERIES AND CONTINUED FRACTIONS
JOURNAL OF RAMANUJAN SOCIETY OF MATHEMATICS AND MATHEMATICAL SCIENCES, 2022 In this paper, making use of certain known identities, we have established some result involving q-series and continued fractions.
Garima Pant, Krishna Bhadur Chand
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Transformation formulas for multivariable basic hypergeometric series [PDF]
Methods and Applications of Analysis, 1999 Latex2e, 17 ...
T. H. Baker, Peter J. Forrester
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On convergence of basic hypergeometric series [PDF]
, 2015 6 ...
Toshio Oshima
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A bilateral series involving basic hypergeometric functions [PDF]
, 2003 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.
Hjalmar Rosengren
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Bilateral Basic Hypergeometric Series: A Study
Anusandhaan - Vigyaan Shodh Patrika, 2018 In the present work, certain transformations and summation formulae for basic bilateral hypergeometric series have been discussed. This study also gives the method of obtaining new transformations and summation formulae for basic bilateral hypergeometric series. Some of the applications have been mentioned.
Aditya Agnihotri
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