Search Results - "Other basic hypergeometric functions and integrals in several variables"

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

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Access URL: 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

Authors: Hari M. Srivastava Shy-Der Lin

Source: Acta Applicandae Mathematicae. 86:309-327

Subject Terms: 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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Access URL: 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

Authors: Vyacheslav P. Spiridonov

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

Subject Terms: 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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Access URL: 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 \(A_{m}\)

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

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

Authors: Hjalmar Rosengren Christian Krattenthaler

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

Subject Terms: 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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Access URL: 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.

Authors: Zudilin, W. Faculty of Science, School of Mathematical and Physical Sciences

Contributors: Zudilin, W. Faculty of Science, School of Mathematical and Physical Sciences

Source: Russian Mathematical Surveys. 58:1-29

Subject Terms: 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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Access URL: 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.

Authors: CHU, Wenchang

Source: Constructive Approximation. 18:579-597

Subject Terms: 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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Access URL: 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

Authors: Helmut Prodinger Tuwani A. Tsifhumulo

Source: Annals of Combinatorics. 6:181-194

Subject Terms: 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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Access URL: 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

Authors: J. Van der Jeugt

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

Subject Terms: 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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Access URL: 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

Authors: Kevin W. J. Kadell

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

Subject Terms: 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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Access URL: 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

Authors: I M Gel'fand Mark Iosifovich Graev

Source: Russian Mathematical Surveys. 56:615-647

Subject Terms: 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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Access URL: 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 \(\text{u}_q(2)\)

Authors: Sigitas Ališauskas

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

Subject Terms: 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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Access URL: 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

Authors: Ping Zhou

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

Subject Terms: 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

File Description: application/xml

Access URL: 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 \(A_r\)

Authors: Michael J. Schlosser

Source: The Ramanujan Journal. 3:405-461

Subject Terms: 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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Access URL: 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

Authors: Gaurav Bhatnagar

Source: The Ramanujan Journal. 3:175-203

Subject Terms: 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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Access URL: 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

Authors: Michael J. Schlosser Christian Krattenthaler

Source: Discrete Mathematics. 204:249-279

Subject Terms: 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

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Access URL: 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

Authors: Gaurav Bhatnagar

Source: Ramanujan Journal. 3(2):175-203

Subject Terms: 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

File Description: application/xml

Access URL: 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 \(U(n)\)

Authors: Stephen C. Milne Verne E. Leininger

Source: Discrete Mathematics. 204:281-317

Subject Terms: 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

File Description: application/xml

Access URL: 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

Authors: Per W. Karlsson Hari M. Srivastava

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

Subject Terms: 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

File Description: application/xml

Access URL: 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

Authors: Vadim B. Kuznetsov Evgueni K. Sklyanin

Source: The Ramanujan Journal. 3:5-35

Subject Terms: 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

File Description: application/xml

Access URL: 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