Search Results - "Basic hypergeometric functions associated with root systems"

Infinite Families of Exact Sums of Squares Formulas, Jacobi Elliptic Functions, Continued Fractions, and Schur Functions: Infinite families of exact sums of squares formulas, Jacobi elliptic functions, continued fractions, and Schur functions

Authors: Milne, Stephen C.

Source: Developments in Mathematics ISBN: 9781441952134

Subject Terms: Mathematics - Number Theory, Other basic hypergeometric functions and integrals in several variables, Exact enumeration problems, generating functions, 0102 computer and information sciences, 01 natural sciences, Elliptic functions and integrals, Binomial coefficients, factorials, \(q\)-identities, Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Theta series, Weil representation, theta correspondences, Number Theory (math.NT), 0101 mathematics, Sums of squares and representations by other particular quadratic forms, Basic hypergeometric functions associated with root systems

File Description: application/xml

Access URL: http://arxiv.org/abs/math/0008068

Unit Circle Elliptic Beta Integrals: Unit circle elliptic beta integrals

Authors: Van Diejen, J.F. Spiridonov, V.P.

Source: Articulos_ANID
Agencia Nacional de Investigación y Desarrollo
instacron:ANID
RAMANUJAN JOURNAL
Artículos CONICYT
CONICYT Chile
instacron:CONICYT
Conicyt_qa
ANID

Subject Terms: elliptic gamma functions, 33D99, 33E20, 01 natural sciences, \(q\)-gamma functions, \(q\)-beta functions and integrals, Bibasic functions and multiple bases, Mathematics - Classical Analysis and ODEs, 0103 physical sciences, Jacobi forms, Classical Analysis and ODEs (math.CA), FOS: Mathematics, 0101 mathematics, elliptic hypergeometric integrals, Basic hypergeometric functions associated with root systems, beta integrals

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Access URL: http://arxiv.org/pdf/math/0309279
http://arxiv.org/abs/math/0309279
https://arxiv.org/pdf/math/0309279.pdf
http://core.ac.uk/display/2573348
https://arxiv.org/abs/math/0309279
https://link.springer.com/article/10.1007/s11139-005-4846-x
http://ui.adsabs.harvard.edu/abs/2003math......9279V/abstract
https://link.springer.com/content/pdf/10.1007/s11139-005-4846-x.pdf
https://hdl.handle.net/10533/176248
http://hdl.handle.net/10533/176248
https://repositorio-qa.anid.cl/handle/10533/176248

A Conjecture about Raising Operators for Macdonald Polynomials: A conjecture about raising operators for Macdonald polynomials

Authors: Jun'ichi Shiraishi

Source: Letters in Mathematical Physics. 73:71-81

Subject Terms: basic hypergeometric series, 01 natural sciences, Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.), raising operators, Mathematics - Quantum Algebra, 0103 physical sciences, FOS: Mathematics, Mathematics - Combinatorics, Quantum Algebra (math.QA), 33D15, 81R50, Macdonald polynomials, Combinatorics (math.CO), 0101 mathematics, Quantum groups and related algebraic methods applied to problems in quantum theory, Basic hypergeometric functions associated with root systems

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Access URL: http://arxiv.org/pdf/math/0503727
http://arxiv.org/abs/math/0503727
https://link.springer.com/article/10.1007/s11005-005-7648-6
https://ui.adsabs.harvard.edu/abs/2005LMaPh..73...71S/abstract
https://arxiv.org/abs/math/0503727
https://core.ac.uk/display/21931096
https://arxiv.org/pdf/math/0503727

BCn-symmetric polynomials: BC\(_n\)-symmetric polynomials

Authors: Rains, Eric M.

Source: Transformation Groups. 10:63-132

Subject Terms: Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.), Orthogonal polynomials and functions in several variables expressible in terms of basic hypergeometric functions in one variable, 01 natural sciences, Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.), binomial formula, \(BC_n\)-symmetric interpolation polynomials, multivariable Askey-Wilson polynomials, Mathematics - Quantum Algebra, FOS: Mathematics, Mathematics - Combinatorics, Quantum Algebra (math.QA), Macdonald polynomials, Combinatorics (math.CO), 0101 mathematics, Koornwinder polynomials, Basic hypergeometric functions associated with root systems

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Access URL: https://authors.library.caltech.edu/81978/2/0112035.pdf
http://arxiv.org/abs/math/0112035
https://link.springer.com/article/10.1007/s00031-005-1003-y
https://link.springer.com/content/pdf/10.1007/s00031-005-1003-y.pdf

Euler transformation formula for multiple basic hypergeometric series of type A and some applications: Euler transformation formula for multiple basic hypergeometric series of type \(A\) and some applications

Authors: Yasushi Kajihara

Source: Advances in Mathematics. 187:53-97

Subject Terms: Mathematics(all), Heine transformation, Pfaff-Saalschütz summation formula, Hypergeometric functions associated with root systems, Multiple basic hypergeometric series of type A, Gauß summation formula, 01 natural sciences, Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.), Watson type transformation, Pfaff–Saalschutz summation, basic hypergeometric series associated to root systems, Euler transformation, Macdonald polynomials, 0101 mathematics, Bailey–Jackson type transformation–summation formula, Bailey's transformation formula, Basic hypergeometric functions associated with root systems, Watson's transformation formula

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Access URL: https://zbmath.org/2093004
https://doi.org/10.1016/j.aim.2003.08.012
https://dialnet.unirioja.es/servlet/articulo?codigo=928457
https://www.sciencedirect.com/science/article/pii/S0001870803002603
https://core.ac.uk/display/82561434
https://www.infona.pl/resource/bwmeta1.element.elsevier-6c111077-163f-3382-9c84-c08a24fcdd85
https://www.sciencedirect.com/science/article/abs/pii/S0001870803002603

Multivariate basic hypergeometric series associated to root systems of type Am: Multivariate basic hypergeometric series associated to root systems of type \(A_{m}\)

Authors: Medhat A. Rakha

Source: Journal of Mathematical Analysis and Applications. 294:181-195

Subject Terms: Integral transformations, Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.), hypergeometric series very well poised on Lie algebras, q-beta integrals, Applied Mathematics, Other basic hypergeometric functions and integrals in several variables, \(q\)-series, 0102 computer and information sciences, \(q\)-beta integrals, q-series, 01 natural sciences, Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.), integral transformations, Hypergeometric series very well poised on Lie algebras, \(q\)-gamma functions, \(q\)-beta functions and integrals, multivariate basic hypergeometric series associated with root systems, 0101 mathematics, Analysis, Basic hypergeometric functions associated with root systems

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Access URL: https://www.sciencedirect.com/science/article/pii/S0022247X04001246
https://squ.pure.elsevier.com/en/publications/multivariate-basic-hypergeometric-series-associated-to-root-syste
https://core.ac.uk/display/82398993
https://www.sciencedirect.com/science/article/abs/pii/S0022247X04001246

Finite Aomoto-Ito-Macdonald sums

Authors: De La Maza, A.C.

Source: Articulos_ANID
Agencia Nacional de Investigación y Desarrollo
instacron:ANID
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
Artículos CONICYT
CONICYT Chile
instacron:CONICYT
Conicyt_qa
ANID

Subject Terms: 0101 mathematics, Trigonometric and exponential sums (general theory), 01 natural sciences, Basic hypergeometric functions associated with root systems, Combinatorial identities, bijective combinatorics

File Description: application/xml; 2648 bytes; text/html

Access URL: https://www.ams.org/proc/2004-132-07/S0002-9939-04-07305-8/S0002-9939-04-07305-8.pdf
https://dialnet.unirioja.es/servlet/articulo?codigo=921180
https://www.jstor.org/stable/4097184
https://www.ams.org/proc/2004-132-07/S0002-9939-04-07305-8/S0002-9939-04-07305-8.pdf
https://www.ams.org/journals/proc/2004-132-07/S0002-9939-04-07305-8/home.html
https://documat.unirioja.es/servlet/articulo?codigo=921180
https://hdl.handle.net/10533/175401
http://hdl.handle.net/10533/175401
https://repositorio-qa.anid.cl/handle/10533/175401

Elliptic hypergeometric series on root systems: Elliptic hypergeometric series on root systems.

Authors: Hjalmar Rosengren

Source: Advances in Mathematics. 181:417-447

Subject Terms: Mathematics(all), Multivariable Bailey transformation, 33D67, 11F50, Elliptic hypergeometric series, 01 natural sciences, Jackson summation, hypergeometric series on root systems, Multivariable Jackson summation, Mathematics - Classical Analysis and ODEs, Bailey transforms, Hypergeometric series on root systems, Mathematics - Quantum Algebra, 0103 physical sciences, Jacobi forms, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Quantum Algebra (math.QA), elliptic hypergeometric series, 0101 mathematics, Basic hypergeometric functions associated with root systems

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Access URL: http://arxiv.org/abs/math/0207046
https://research.chalmers.se/en/publication/23706
https://www.sciencedirect.com/science/article/abs/pii/S0001870803000719
https://www.sciencedirect.com/science/article/pii/S0001870803000719

Summations and transformations for multiple basic and elliptic hypergeometric series by determinant evaluations

Authors: Michael J. Schlosser Hjalmar Rosengren

Source: Indagationes Mathematicae. 14:483-513

Subject Terms: 1010 Mathematics, Mathematics(all), 1010 Mathematik, basic hypergeometric series, 01 natural sciences, \(q\)-gamma functions, \(q\)-beta functions and integrals, Mathematics - Classical Analysis and ODEs, Mathematics - Quantum Algebra, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Mathematics - Combinatorics, Quantum Algebra (math.QA), Combinatorics (math.CO), 33D67 (Primary) 05A30, 33D05 (Secondary), 0101 mathematics, Basic hypergeometric functions associated with root systems

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Access URL: http://arxiv.org/abs/math/0304249
https://zbmath.org/2077016
https://doi.org/10.1016/s0019-3577(03)90058-9
https://ucrisportal.univie.ac.at/de/publications/d803c47c-5ec9-4121-9077-521d66aca8b2
https://research.chalmers.se/en/publication/102509
https://www.sciencedirect.com/science/article/pii/S0019357703900589
https://www.arxiv-vanity.com/papers/math/0304249/
https://www.sciencedirect.com/science/article/abs/pii/S0019357703900589

Some limit relations in the A1 tableau of Dunkl-Cherednik operators: Some limit relations in the \(A_{1}\) tableau of Dunkl-Cherednik operators

Authors: Renato Alvarez-Nodarse Universidad de Sevilla. Departamento de Análisis Matemático Ministerio de Ciencia y Tecnología (MCYT). España et al.

Contributors: Renato Alvarez-Nodarse Universidad de Sevilla. Departamento de Análisis Matemático Ministerio de Ciencia y Tecnología (MCYT). España et al.

Source: idUS. Depósito de Investigación de la Universidad de Sevilla
Universidad de Sevilla (US)
instname

Subject Terms: Mathematics(all), Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.), root systems, Hypergeometric functions associated with root systems, basic hypergeometric series, 01 natural sciences, Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), q-polynomials, 0103 physical sciences, Dunkl-Cherednik operators, 0101 mathematics, Connections of basic hypergeometric functions with quantum groups, Chevalley groups, \(p\)-adic groups, Hecke algebras, and related topics, \(q\)-polynomials, Basic hypergeometric functions associated with root systems, hypergeometric functions

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Access URL: https://idus.us.es/xmlui/handle/11441/41721
http://hdl.handle.net/11441/41721
https://idus.us.es/handle/11441/41721
https://zbmath.org/2077005
https://doi.org/10.1016/s0019-3577(03)90047-4
https://www.sciencedirect.com/science/article/pii/S0019357703900474
https://idus.us.es/bitstream/11441/41721/1/Some%20limit%20relations%20in%20the%20A1%20tableau%20of%20Dunkl-Cherednik%20operators.pdf
https://idus.us.es/handle/11441/41721
https://www.sciencedirect.com/science/article/abs/pii/S0019357703900474
http://hera.ugr.es/doi/15059510.pdf

Multiple elliptic hypergeometric series. An approach from the Cauchy determinant

Authors: Masatoshi Noumi Yasushi Kajihara

Source: Indagationes Mathematicae. 14:395-421

Subject Terms: duality transformation, Mathematics(all), Cauchy determinant formula, 01 natural sciences, Other hypergeometric functions and integrals in several variables, very well-poised multiple hypergeometric series, Basic hypergeometric functions in one variable, \({}_r\phi_s\), Mathematics - Classical Analysis and ODEs, Mathematics - Quantum Algebra, 0103 physical sciences, Bailey transformation, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Quantum Algebra (math.QA), 0101 mathematics, multiple elliptic hypergeometric series, Basic hypergeometric functions associated with root systems

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Access URL: http://arxiv.org/abs/math/0306219
https://zbmath.org/2077012
https://doi.org/10.1016/s0019-3577(03)90054-1
https://www.sciencedirect.com/science/article/pii/S0019357703900541
https://www.sciencedirect.com/science/article/abs/pii/S0019357703900541

A nonterminating 8φ7 summation for the root system Cr: A nonterminating \(_8\phi_7\) summation for the root system \(C_r\).

Authors: Michael J. Schlosser

Source: Journal of Computational and Applied Mathematics. 160:283-296

Subject Terms: 1010 Mathematics, 1010 Mathematik, multiple \(q\)-integrals, \(q\)-series, q-series, 01 natural sciences, Nonterminating 3φ2 summation, root system \(C_r\), Cr series, \(q\)-gamma functions, \(q\)-beta functions and integrals, Mathematics - Quantum Algebra, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Sp(r) series, Quantum Algebra (math.QA), 0101 mathematics, Ar series, Basic hypergeometric functions associated with root systems, U(n) series, Applied Mathematics, determinant method, Computational Mathematics, Nonterminating 8φ7 summation, nonterminating \(_8\phi_7\) summation, Mathematics - Classical Analysis and ODEs, Multiple q-integrals, 33D67 (Primary) 05A30, 33D05 (Secondary)

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Access URL: http://arxiv.org/abs/math/0211151
https://zbmath.org/2006435
https://doi.org/10.1016/s0377-0427(03)00632-0
http://arxiv.org/pdf/math/0211151.pdf
https://arxiv.org/abs/math/0211151
https://www.sciencedirect.com/science/article/abs/pii/S0377042703006320
https://www.sciencedirect.com/science/article/pii/S0377042703006320
https://ui.adsabs.harvard.edu/abs/2003JCoAM.160..283S/abstract

Reduction Formulas for Karlsson–Minton-Type Hypergeometric Functions: Reduction formulas for Karlsson-Minton-type hypergeometric functions

Authors: Hjalmar Rosengren

Source: Constructive Approximation. 20:525-548

Subject Terms: hypergeometric series on root systems, 33D15, 33D67, Karlsson-Minton-type hypergeometric series, Basic hypergeometric functions in one variable, \({}_r\phi_s\), Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, 0101 mathematics, 01 natural sciences, Basic hypergeometric functions associated with root systems

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Access URL: http://arxiv.org/pdf/math/0202232v3.pdf
http://arxiv.org/abs/math/0202232
https://zbmath.org/2132294
https://doi.org/10.1007/s00365-003-0541-6
https://link.springer.com/article/10.1007/s00365-003-0541-6
https://research.chalmers.se/en/publication/23705

Karlsson–Minton type hypergeometric functions on the root system Cn: Karlsson--Minton type hypergeometric functions on the root system \(C_{n}\)

Authors: Hjalmar Rosengren

Source: Journal of Mathematical Analysis and Applications. 281:332-345

Subject Terms: Mathematics - Classical Analysis and ODEs, Applied Mathematics, Classical Analysis and ODEs (math.CA), FOS: Mathematics, 33D67, basic hypergeometric series, 0101 mathematics, 01 natural sciences, Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.), Analysis, Basic hypergeometric functions associated with root systems

File Description: application/xml

Access URL: http://arxiv.org/abs/math/0205108
https://zbmath.org/1956865
https://doi.org/10.1016/s0022-247x(03)00103-3
https://www.sciencedirect.com/science/article/abs/pii/S0022247X03001033
https://www.sciencedirect.com/science/article/pii/S0022247X03001033
https://research.chalmers.se/en/publication/102506

Poincaré Series of the Weyl Groups of the Elliptic Root Systems A 1 (1,1), A 1 (1,1)* and A 2 (1,1): Poincaré series of the Weyl groups of the elliptic root systems \(A_1^{(1,1)}\), \(A_1^{(1,1)^*}\) and \(A_2^{(1,1)}\).

Authors: Tadayoshi Takebayashi

Source: Journal of Algebraic Combinatorics. 17:211-223

Subject Terms: Generators, relations, and presentations of groups, Reflection and Coxeter groups (group-theoretic aspects), elliptic root systems, 0101 mathematics, elliptic Weyl groups, Poincaré series, 01 natural sciences, Basic hypergeometric functions associated with root systems

File Description: application/xml

Access URL: https://link.springer.com/content/pdf/10.1023%2FA%3A1025081404009.pdf
https://zbmath.org/1981397
https://link.springer.com/article/10.1023/A:1025081404009
https://link.springer.com/content/pdf/10.1023/A:1025081404009.pdf

10E9solution to the elliptic Painlev equation: \(_{10}E_9\) solution to the elliptic Painlevé equation.

Authors: Masatoshi Noumi Kenji Kajiwara Tetsu Masuda et al.

Source: Journal of Physics A: Mathematical and General. 36:L263-L272

Subject Terms: Painlevé-type functions, Nonlinear Sciences - Exactly Solvable and Integrable Systems, elliptic Painlevé equation, Multiplicative and other generalized difference equations, non-autonomous deformation, FOS: Physical sciences, 01 natural sciences, Birational automorphisms, Cremona group and generalizations, Mathematics - Quantum Algebra, 0103 physical sciences, Painlevé and other special ordinary differential equations in the complex domain, classification, hierarchies, elliptic curves, FOS: Mathematics, Elliptic curves, elliptic hypergeometric function, Quantum Algebra (math.QA), Discrete version of topics in analysis, Exactly Solvable and Integrable Systems (nlin.SI), 0101 mathematics, Basic hypergeometric functions associated with root systems

File Description: application/xml

Access URL: http://arxiv.org/abs/nlin/0303032
http://iopscience.iop.org/article/10.1088/0305-4470/36/17/102/pdf
https://ui.adsabs.harvard.edu/abs/2003JPhA...36L.263K/abstract
https://iopscience.iop.org/article/10.1088/0305-4470/36/17/102/pdf
https://kyushu-u.pure.elsevier.com/ja/publications/10e9-solution-to-the-elliptic-painlev%C3%A9-equation
https://iopscience.iop.org/article/10.1088/0305-4470/36/17/102

symmetry classification for jackson integrals associated with the root system bc n: Symmetry classification for Jackson integrals associated with the root system \(BC_n\)

Authors: Masahiko Ito

Source: Compositio Mathematica. 136(2):209-216

Subject Terms: Jackson integrals, non-reduced root system, Bailey's very-well-poised \(_6\psi _6\) sum, van Diejen's \(BC_n\)-type sum, Gustafson's \(C_n\)-type sum, Basic hypergeometric functions associated with root systems

File Description: application/xml

Access URL: https://zbmath.org/1908550
https://doi.org/10.1023/a:1022892011301
https://link.springer.com/article/10.1023/A:1022892011301

A Multidimensional Generalization of Shukla's 8ψ8 Summation: A multidimensional generalization of Shukla's \(_8\psi _8\) summation

Authors: Michael J. Schlosser

Source: Constructive Approximation. 19:163-178

Subject Terms: 1010 Mathematics, 33D15, 33D67, 1010 Mathematik, \(q\)-series, basic hypergeometric series, \(U(r)\) series, \(_8\psi_8\) summation, 01 natural sciences, \(_6\phi_5\) summation, Basic hypergeometric functions in one variable, \({}_r\phi_s\), Mathematics - Classical Analysis and ODEs, \(A_r\) series, bilateral series, Mathematics - Quantum Algebra, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Mathematics - Combinatorics, Quantum Algebra (math.QA), Combinatorics (math.CO), 0101 mathematics, Basic hypergeometric functions associated with root systems

File Description: application/xml

Access URL: http://arxiv.org/pdf/math/0103024
http://arxiv.org/abs/math/0103024
https://zbmath.org/1903774
https://doi.org/10.1007/s00365-001-0016-6
https://ucrisportal.univie.ac.at/de/publications/348d34a7-2ebf-4d6f-a128-df0562ad5534
http://ui.adsabs.harvard.edu/abs/2001math......3024S/abstract
https://link.springer.com/article/10.1007/s00365-001-0016-6
https://arxiv.org/pdf/math/0103024v1

The roots of the third Jackson q‐Bessel function: The roots of the third J. Jckson \(q\)-Bessel function

Authors: Abreu, L. D. Bustoz, J. Cardoso, J. L.

Source: International Journal of Mathematics and Mathematical Sciences, Vol 2003, Iss 67, Pp 4241-4248 (2003)

Subject Terms: Basic hypergeometric functions in one variable, \({}_r\phi_s\), QA1-939, 0101 mathematics, 01 natural sciences, Mathematics, Basic hypergeometric functions associated with root systems

File Description: application/xml

Access URL: http://downloads.hindawi.com/journals/ijmms/2003/709476.pdf
https://doaj.org/article/e407503974e04b3089c936304aff5241
http://www.mat.uc.pt/preprints/ps/p0209.pdf
https://www.emis.de/journals/HOA/IJMMS/Volume2003_67/709476.pdf
https://estudogeral.sib.uc.pt/bitstream/10316/11450/1/The%20roots%20of%20the%20third%20Jackson%20q-Bessel%20function.pdf
https://downloads.hindawi.com/journals/ijmms/2003/709476.pdf
https://estudogeral.sib.uc.pt/handle/10316/11450
https://www.hindawi.com/journals/ijmms/2003/709476/
https://hdl.handle.net/10316/11450
https://hdl.handle.net/10316/110959

Summation and transformation formulas for elliptic hypergeometric series: Summation and transformation formulas for elliptic hypergeometric series.

Authors: Warnaar, SO

Source: Constructive Approximation. 18:479-502

Subject Terms: Lattices and Combinatorics, q-analog, bailey, 0102 computer and information sciences, 01 natural sciences, Mathematical Sciences, q-lagrange inversion, 0101 Pure Mathematics, Basic hypergeometric functions in one variable, \({}_r\phi_s\), Mathematics - Quantum Algebra, FOS: Mathematics, Mathematical Logic, Mathematics - Combinatorics, Quantum Algebra (math.QA), elliptic hypergeometric series, 0101 mathematics, Determinants, Basic hypergeometric functions associated with root systems, poised (10)PHI(9) transformations, Orthogonal polynomials and functions in several variables expressible in terms of basic hypergeometric functions in one variable, U(N), combinatorial identities, Elliptic functions and integrals, \(q\)-calculus and related topics, Set Theory, Combinatorics (math.CO), elliptic functions, elliptic hypergeomeytric series, Primary 33D15, 33D67, 33E05, Secondary 05A30

File Description: application/xml; application/pdf

Access URL: http://arxiv.org/pdf/math/0001006
http://arxiv.org/abs/math/0001006
https://zbmath.org/1885732
https://doi.org/10.1007/s00365-002-0501-6
https://ui.adsabs.harvard.edu/abs/2000math......1006W/abstract
https://arxiv.org/pdf/math/0001006
https://arxiv.org/abs/math/0001006
https://espace.library.uq.edu.au/view/UQ:188975
https://link.springer.com/article/10.1007/s00365-002-0501-6
https://minerva-access.unimelb.edu.au/handle/11343/26188