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

Συγγραφείς: Milne, Stephen C.

Πηγή: Developments in Mathematics ISBN: 9781441952134

Θεματικοί όροι: 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

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: http://arxiv.org/abs/math/0008068

Some Closed-Form Evaluations of Multiple Hypergeometric and q-Hypergeometric Series: Some closed-form evaluations of multiple hypergeometric and \(q\)-hypergeometric series

Συγγραφείς: Hari M. Srivastava, Shy-Der Lin

Πηγή: Acta Applicandae Mathematicae. 86:309-327

Θεματικοί όροι: multiple hypergeometric and \(q\)-hypergeometric series, summation formulas, Other hypergeometric functions and integrals in several variables, Classical hypergeometric functions, \({}_2F_1\), Appell, Horn and Lauricella functions, Generalized hypergeometric series, \({}_pF_q\), Appel and Lauricella series, Basic hypergeometric functions in one variable, \({}_r\phi_s\), Other basic hypergeometric functions and integrals in several variables, transformation and reduction formulas, 0101 mathematics, 01 natural sciences

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Σύνδεσμος πρόσβασης: https://link.springer.com/article/10.1007%2Fs10440-004-7465-4
https://link.springer.com/content/pdf/10.1007/s10440-004-7465-4.pdf

Theta hypergeometric integrals

Συγγραφείς: Vyacheslav P. Spiridonov

Πηγή: St. Petersburg Mathematical Journal. 15:929-968

Θεματικοί όροι: Other basic hypergeometric functions and integrals in several variables, Hypergeometric functions associated with root systems, theta hypergeometric integrals, 01 natural sciences, 33Dxx, 33E20, 39A13, Other hypergeometric functions and integrals in several variables, Elliptic functions and integrals, \(q\)-gamma functions, \(q\)-beta functions and integrals, Mathematics - Classical Analysis and ODEs, 0103 physical sciences, Elliptic integrals as hypergeometric functions, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Jacobi theta functions, multiple hypergeometric integrals, 0101 mathematics

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Σύνδεσμος πρόσβασης: http://arxiv.org/pdf/math/0303205v2.pdf
http://arxiv.org/abs/math/0303205
https://zbmath.org/2165587
https://doi.org/10.1090/s1061-0022-04-00839-8
https://www.ams.org/spmj/2004-15-06/S1061-0022-04-00839-8/S1061-0022-04-00839-8.pdf
https://www.ams.org/journals/spmj/2004-15-06/S1061-0022-04-00839-8/home.html
https://www.arxiv-vanity.com/papers/math/0303205/
https://arxiv.org/pdf/math/0303205
https://pure.mpg.de/pubman/faces/ViewItemOverviewPage.jsp?itemId=item_3124942

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

Συγγραφείς: Medhat A. Rakha

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

Θεματικοί όροι: 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

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: 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

On a hypergeometric identity of Gelfand, Graev and Retakh: On a hypergeometric identity of Gelfand, Graev and Retakh.

Συγγραφείς: Hjalmar Rosengren, Christian Krattenthaler

Πηγή: Journal of Computational and Applied Mathematics. 160:147-158

Θεματικοί όροι: Ramanujan's 1ψ1 summation, multiple hypergeometric series, Generalized hypergeometric series, \({}_pF_q\), Applied Mathematics, Other basic hypergeometric functions and integrals in several variables, basic hypergeometric series, Basic hypergeometric series, 16. Peace & justice, 01 natural sciences, Other hypergeometric functions and integrals in several variables, Computational Mathematics, Chu-Vandermonde summation Pfaff-Saalschütz summation, Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Ramanujan's \(_{1}{\psi}_1\) summation, 0101 mathematics, Multiple hypergeometric series, 33C70 (Primary) 33C20 33D70 (Secondary), Chu–Vandermonde summation Pfaff–Saalschütz summation

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Σύνδεσμος πρόσβασης: http://arxiv.org/abs/math/0303061
https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.234.221&rep=rep1&type=pdf
https://www.sciencedirect.com/science/article/pii/S0377042703006204
https://ui.adsabs.harvard.edu/abs/2003JCoAM.160..147K/abstract
https://www.sciencedirect.com/science/article/abs/pii/S0377042703006204
https://research.chalmers.se/publication/102507

Algebraic relations for multiple zeta values: Algebraic relations for multiple zeta values.

Συγγραφείς: Zudilin, W.

Συνεισφορές: Faculty of Science, School of Mathematical and Physical Sciences

Πηγή: Russian Mathematical Surveys. 58:1-29

Θεματικοί όροι: Irrationality, linear independence over a field, polynomial relations, mathematics, Multiple Dirichlet series and zeta functions and multizeta values, Other basic hypergeometric functions and integrals in several variables, Riemann zeta function, 0101 mathematics, 01 natural sciences, Polylogarithms and relations with \(K\)-theory

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Σύνδεσμος πρόσβασης: http://carma.newcastle.edu.au/wadim/PS/mzv_rms.pdf
http://ui.adsabs.harvard.edu/abs/2003RuMaS..58....1Z/abstract

The Saalschütz chain reactions and bilateral basic hypergeometric series: The Saalschütz chain reactions and bilateral basic hypergeometric series.

Συγγραφείς: CHU, Wenchang

Πηγή: Constructive Approximation. 18:579-597

Θεματικοί όροι: multiple basic hypergeometric series, bilateral \(q\)-hyergeometric series, Basic hypergeometric functions in one variable, \({}_r\phi_s\), \(q\)-calculus and related topics, Other basic hypergeometric functions and integrals in several variables, Saalschütz chain reactions, 0101 mathematics, 01 natural sciences, BILATERAL Q-SERIES

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Σύνδεσμος πρόσβασης: https://zbmath.org/1885737
https://doi.org/10.1007/s00365-001-0026-4
https://link.springer.com/content/pdf/10.1007%2Fs00365-001-0026-4.pdf
https://link.springer.com/article/10.1007/s00365-001-0026-4
https://hdl.handle.net/11587/369134

On q-Olivier Functions: On \(q\)-Olivier functions

Συγγραφείς: Helmut Prodinger, Tuwani A. Tsifhumulo

Πηγή: Annals of Combinatorics. 6:181-194

Θεματικοί όροι: Combinatorial probability, permutations, Other basic hypergeometric functions and integrals in several variables, Exact enumeration problems, generating functions, Olivier functions, 0102 computer and information sciences, 0101 mathematics, 01 natural sciences, geometric probabilities, words

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Σύνδεσμος πρόσβασης: https://zbmath.org/1889234
https://doi.org/10.1007/pl00012585
https://link.springer.com/article/10.1007/PL00012585

Transformation formula for a double Clausenian hypergeometric series, its q-analogue, and its invariance group: Transformation formula for a double Clausenian hypergeometric series, its \(q\)-analogue, and its invariance group

Συγγραφείς: J. Van der Jeugt

Πηγή: Journal of Computational and Applied Mathematics. 139:65-73

Θεματικοί όροι: summation formulas, invariance group, Hypergeometric integrals and functions defined by them (\(E\), \(G\), \(H\) and \(I\) functions), transformation, Applied Mathematics, Other basic hypergeometric functions and integrals in several variables, reduction, Connections of hypergeometric functions with groups and algebras, and related topics, basic hypergeometric series, Transformation formulae, 01 natural sciences, Double basic hypergeometric series, Double hypergeometric series, Transformation group, Other hypergeometric functions and integrals in several variables, Computational Mathematics, 0101 mathematics

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Σύνδεσμος πρόσβασης: https://biblio.ugent.be/publication/161957
https://dl.acm.org/doi/10.1016/S0377-0427%2801%2900389-2
http://ui.adsabs.harvard.edu/abs/2002JCoAM.139...65V/abstract
https://www.sciencedirect.com/science/article/pii/S0377042701003892
http://www.sciencedirect.com/science/article/pii/S0377042701003892

A Simple Proof of an Aomoto-Type Extension of Askey's Last Conjectured Selberg q-Integral: A simple proof of an Aomoto-type extension of Askey's last conjectured Selberg \(q\)-integral

Συγγραφείς: Kevin W. J. Kadell

Πηγή: Journal of Mathematical Analysis and Applications. 261:419-440

Θεματικοί όροι: Aomoto-type extensions, Selberg's integral, Applied Mathematics, Other basic hypergeometric functions and integrals in several variables, Selberg \(q\)-integrals, q-transportation theory for the root system An−1, Aomoto-type extension, 0101 mathematics, 01 natural sciences, Analysis

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Σύνδεσμος πρόσβασης: https://zbmath.org/1676044
https://doi.org/10.1006/jmaa.2000.7180
https://www.sciencedirect.com/science/article/abs/pii/S0022247X00971804
https://www.sciencedirect.com/science/article/pii/S0022247X00971804
https://core.ac.uk/display/82223453

$ \mathscr N$-functions and their relationship with solutions of general hypergeometric systems andGG-systems: \({\mathcal N}\)-functions and their relationships with solutions of general hypergeometric systems and \(GG\)-systems

Συγγραφείς: I M Gel'fand, Mark Iosifovich Graev

Πηγή: Russian Mathematical Surveys. 56:615-647

Θεματικοί όροι: Other hypergeometric functions and integrals in several variables, Other basic hypergeometric functions and integrals in several variables, Moduli and deformations for ordinary differential equations (e.g., Knizhnik-Zamolodchikov equation), 0101 mathematics, 01 natural sciences

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Σύνδεσμος πρόσβασης: https://iopscience.iop.org/article/10.1070/RM2001v056n04ABEH000414
http://ui.adsabs.harvard.edu/abs/2001RuMaS..56..615G/abstract
http://iopscience.iop.org/article/10.1070/RM2001v056n04ABEH000414/pdf

The multiple sum formulas for 12j coefficients of SU(2) and uq(2): The triple sum formulas for \(9j\) coefficients of SU(2) and \(\text{u}_q(2)\)

Συγγραφείς: Sigitas Ališauskas

Πηγή: Journal of Mathematical Physics. 43:1547-1568

Θεματικοί όροι: Quantum Physics, Generalized hypergeometric series, \({}_pF_q\), Other basic hypergeometric functions and integrals in several variables, FOS: Physical sciences, Quantum groups (quantized enveloping algebras) and related deformations, Connections of hypergeometric functions with groups and algebras, and related topics, Mathematical Physics (math-ph), 81R,33C,33D, Kampé de Fériet functions, Dougall's summation formula, 01 natural sciences, Finite-dimensional groups and algebras motivated by physics and their representations, Basic hypergeometric functions in one variable, \({}_r\phi_s\), Chu-Vandermonde summation formulas, Mathematics - Quantum Algebra, 0103 physical sciences, FOS: Mathematics, Quantum Algebra (math.QA), hypergeometric \(_5\varphi_4\) series, 0101 mathematics, Wigner \(9j\) coefficients, Quantum Physics (quant-ph), Connections of basic hypergeometric functions with quantum groups, Chevalley groups, \(p\)-adic groups, Hecke algebras, and related topics, Quantum groups and related algebraic methods applied to problems in quantum theory, Mathematical Physics

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Σύνδεσμος πρόσβασης: http://arxiv.org/pdf/math/9912142
http://arxiv.org/abs/math/9912142
https://zbmath.org/1639428
https://doi.org/10.1063/1.1312198
https://arxiv.org/pdf/math/9912142
https://www.arxiv-vanity.com/papers/math/9912142/
https://arxiv.org/abs/math/9912142
https://aip.scitation.org/doi/10.1063/1.1312198
http://ui.adsabs.harvard.edu/abs/2000JMP....41.7589A/abstract
https://scitation.aip.org/content/aip/journal/jmp/41/11/10.1063/1.1312198

Explicit Construction of Multivariate Padé Approximants for a q-Logarithm Function: Explicit construction of multivariate Padé approximants for a \(q\)-logarithm function

Συγγραφείς: Ping Zhou

Πηγή: Journal of Approximation Theory. 103:18-28

Θεματικοί όροι: Mathematics(all), Numerical Analysis, \(q\)-logarithm function, multivariate Padé approximants, Applied Mathematics, functional equations, Other basic hypergeometric functions and integrals in several variables, q-logarithm functions, functional equation, 0101 mathematics, Padé approximation, 01 natural sciences, Analysis

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Σύνδεσμος πρόσβασης: https://www.sciencedirect.com/science/article/pii/S0021904599934093
https://www.sciencedirect.com/science/article/abs/pii/S0021904599934093
https://core.ac.uk/display/82181217

Some New Applications of Matrix Inversions in A r: Some new applications of matrix inversions in \(A_r\)

Συγγραφείς: Michael J. Schlosser

Πηγή: The Ramanujan Journal. 3:405-461

Θεματικοί όροι: Other basic hypergeometric functions and integrals in several variables, \(q\)-Rothe summations, 101002 Analysis, 101012 Combinatorics, 0102 computer and information sciences, \(q\)-Abel summations, 01 natural sciences, multiple \(q\)-series, \(q\)-calculus and related topics, multidimensional matrix inversions, 101012 Kombinatorik, Theory of matrix inversion and generalized inverses, 0101 mathematics, Combinatorial identities, bijective combinatorics

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Σύνδεσμος πρόσβασης: https://zbmath.org/1406511
https://doi.org/10.1023/a:1009809424076
https://ucrisportal.univie.ac.at/de/publications/10f24b15-f9c5-4223-8bba-8ccd1081a8d8
https://link.springer.com/article/10.1023/A%3A1009809424076

Dn Basic Hypergeometric Series: \(D_n\) basic hypergeometric series

Συγγραφείς: Gaurav Bhatnagar

Πηγή: The Ramanujan Journal. 3:175-203

Θεματικοί όροι: multiple basic hypergeometric series, Combinatorial aspects of partitions of integers, Basic hypergeometric functions in one variable, \({}_r\phi_s\), Other basic hypergeometric functions and integrals in several variables, Rogers-Selberg function, 0101 mathematics, 01 natural sciences, Combinatorial identities, bijective combinatorics

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Σύνδεσμος πρόσβασης: https://link.springer.com/content/pdf/10.1023/A:1006997424561.pdf
https://link.springer.com/article/10.1023/A%3A1006997424561

A new multidimensional matrix inverse with applications to multiple q-series: A new multidimensional matrix inverse with applications to multiple \(q\)-series

Συγγραφείς: Michael J. Schlosser, Christian Krattenthaler

Πηγή: Discrete Mathematics. 204:249-279

Θεματικοί όροι: q-Rothe identities, Matrix inversion, Other basic hypergeometric functions and integrals in several variables, basic hypergeometric series, Basic hypergeometric series, MacMahon's Master Theorem, \(q\)-Rothe identities, 01 natural sciences, matrix inversion, Theoretical Computer Science, Other hypergeometric functions and integrals in several variables, Inverse relations, Binomial coefficients, factorials, \(q\)-identities, Basic hypergeometric functions in one variable, \({}_r\phi_s\), \(q\)-calculus and related topics, inverse relations, \(q\)-Abel identities, Discrete Mathematics and Combinatorics, Theory of matrix inversion and generalized inverses, q-Abel identities, 0101 mathematics, Combinatorial identities, bijective combinatorics

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://zbmath.org/1331476
https://doi.org/10.1016/s0012-365x(98)00374-4
https://www.sciencedirect.com/science/article/pii/S0012365X98003744
https://dblp.uni-trier.de/db/journals/dm/dm204.html#KrattenthalerS99
https://doi.org/10.1016/S0012-365X(98)00374-4
https://www.sciencedirect.com/science/article/abs/pii/S0012365X98003744

dn basic hypergeometric series: \(D_n\) basic hypergeometric series

Συγγραφείς: Gaurav Bhatnagar

Πηγή: Ramanujan Journal. 3(2):175-203

Θεματικοί όροι: multiple basic hypergeometric series, Combinatorial aspects of partitions of integers, Basic hypergeometric functions in one variable, \({}_r\phi_s\), Other basic hypergeometric functions and integrals in several variables, Rogers-Selberg function, Combinatorial identities, bijective combinatorics

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://link.springer.com/content/pdf/10.1023/A:1006997424561.pdf
https://link.springer.com/article/10.1023/A%3A1006997424561

Expansions for (q)∞n2+2n and basic hypergeometric series in U(n): Expansions for \((q)_\infty^{n^2+2n}\) and basic hypergeometric series in \(U(n)\)

Συγγραφείς: Stephen C. Milne, Verne E. Leininger

Πηγή: Discrete Mathematics. 204:281-317

Θεματικοί όροι: Unitary groups \(U(n)\), \(q\)-Whipple transformations, Other basic hypergeometric functions and integrals in several variables, Dihedral group symmetries, 01 natural sciences, η-functions, Very-well-poised on unitary groups U(n + 1), U(n + 1) q-Whipple transformations, Theoretical Computer Science, \(\eta\)-functions, dihedral group symmetries, Algebraic combinatorics, \(q\)-calculus and related topics, Discrete Mathematics and Combinatorics, Multiple basic hypergeometric series, 0101 mathematics, Macdonald identities, Combinatorial identities, bijective combinatorics

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://zbmath.org/1331477
https://doi.org/10.1016/s0012-365x(98)00375-6
https://dblp.uni-trier.de/db/journals/dm/dm204.html#LeiningerM99
https://doi.org/10.1016/S0012-365X(98)00375-6
https://www.sciencedirect.com/science/article/pii/S0012365X98003756
https://www.sciencedirect.com/science/article/abs/pii/S0012365X98003756

Transformations of Multipleq-Series with Quasi-Arbitrary Terms: Transformations of multiple \(q\)-series with quasi-arbitrary terms

Συγγραφείς: Per W. Karlsson, Hari M. Srivastava

Πηγή: Journal of Mathematical Analysis and Applications. 231:241-254

Θεματικοί όροι: basic Pochhammer symbols, Applied Mathematics, Other basic hypergeometric functions and integrals in several variables, transformation formulas, 0101 mathematics, basic hypergeometric summation formulas, 01 natural sciences, Analysis

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: http://www.sciencedirect.com/science/article/pii/S0022247X98962175
https://core.ac.uk/display/82453644
https://www.sciencedirect.com/science/article/pii/S0022247X98962175

Separation of Variables and Integral Relations for Special Functions: Separation of variables and integral relations for special functions

Συγγραφείς: Vadim B. Kuznetsov, Evgueni K. Sklyanin

Πηγή: The Ramanujan Journal. 3:5-35

Θεματικοί όροι: product formulas, Mathematics - Classical Analysis and ODEs, Lamé, Mathieu, and spheroidal wave functions, Other basic hypergeometric functions and integrals in several variables, Mathematics - Quantum Algebra, 0103 physical sciences, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.), Quantum Algebra (math.QA), method of separation of variables, 0101 mathematics, 01 natural sciences

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Σύνδεσμος πρόσβασης: http://arxiv.org/pdf/q-alg/9705006
http://arxiv.org/abs/q-alg/9705006
https://arxiv.org/abs/q-alg/9705006
https://arxiv.org/pdf/q-alg/9705006
https://link.springer.com/content/pdf/10.1023/A:1009880307186.pdf
http://ui.adsabs.harvard.edu/abs/1997q.alg.....5006K/abstract
https://link.springer.com/article/10.1023/A%3A1009880307186