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

Matrix models for multilevel Heckman–Opdam and multivariate Bessel measures: Matrix models for multilevel Heckman-Opdam and multivariate Bessel measures

Authors: Sun, Yi

Source: Annales de l'Institut Henri Poincaré, Probabilités et Statistiques. 61

Subject Terms: Jacobi ensemble, Random matrices (algebraic aspects), Generalized hypergeometric series, \({}_pF_q\), Probability (math.PR), FOS: Physical sciences, hypergeometric function, Connections of hypergeometric functions with groups and algebras, and related topics, Mathematical Physics (math-ph), random matrix theory, Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Random matrices (probabilistic aspects), Other hypergeometric functions and integrals in several variables, 15B52 (primary), 60B20, 33C67 (secondary), Wishart ensemble, FOS: Mathematics, Random fields, Representation Theory (math.RT), Mathematics - Probability, Mathematical Physics, Mathematics - Representation Theory

File Description: application/xml

Access URL: http://arxiv.org/abs/1609.09096
https://zbmath.org/8013054
https://doi.org/10.1214/22-aihp1296

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

File Description: application/xml

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

File Description: application/xml

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

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

File Description: application/xml

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

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

File Description: application/xml

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

$ \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

File Description: application/xml

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

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

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

File Description: application/xml

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

Series identities and associated families of generating functions

Authors: Kung-Yu Chen Hari M. Srivastava

Source: Journal of Mathematical Analysis and Applications. 311:582-599

Subject Terms: Hypergeometric functions and polynomials, Generalized hypergeometric series, \({}_pF_q\), hypergeometric functions and polynomials, Applied Mathematics, Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable, series identities, Other special orthogonal polynomials and functions, double series identities, 01 natural sciences, Generating functions, Other hypergeometric functions and integrals in several variables, Quadratic transformations, generating functions, Pfaff–Saalschütz theorem, Whipple's transformation, 0101 mathematics, Series identities, hypergeometric functions in two variables, Analysis

File Description: application/xml

Access URL: https://zbmath.org/2217433
https://doi.org/10.1016/j.jmaa.2005.03.030
https://www.sciencedirect.com/science/article/pii/S0022247X05001903
https://core.ac.uk/display/82178105
https://www.sciencedirect.com/science/article/abs/pii/S0022247X05001903
http://ui.adsabs.harvard.edu/abs/2005JMAA..311..582C/abstract

Bivariate hypergeometric D-modules: Bivariate hypergeometric \(D\)-modules

Authors: Dickenstein, A. Matusevich, L.F. Sadykov, T.

Source: Adv. Math. 2005;196(1):78-123
Biblioteca Digital (UBA-FCEN)
Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
instacron:UBA-FCEN

Subject Terms: Mathematics(all), Overdetermined systems of PDEs with variable coefficients, 0102 computer and information sciences, 01 natural sciences, Holonomic D-module, holonomic \(D\)-modules, Other hypergeometric functions and integrals in several variables, holonomic rank, Mathematics - Algebraic Geometry, Appell, Horn and Lauricella functions, Sheaves of differential operators and their modules, \(D\)-modules, Holonomic rank, Horn systems, FOS: Mathematics, Hypergeometric function, 0101 mathematics, Horn system, Toric varieties, Newton polyhedra, Okounkov bodies, Algebraic Geometry (math.AG), hypergeometric functions

File Description: application/xml; application/pdf

Access URL: http://arxiv.org/abs/math/0310003
https://zbmath.org/2207380
https://doi.org/10.1016/j.aim.2004.08.012
https://core.ac.uk/display/82589113
https://dialnet.unirioja.es/servlet/articulo?codigo=1268660
https://www.sciencedirect.com/science/article/pii/S0001870804002828
https://www.sciencedirect.com/science/article/abs/pii/S0001870804002828
http://hdl.handle.net/20.500.12110/paper_00018708_v196_n1_p78_Dickenstein

The continuous symmetric Hahn polynomials found in Ramanujan's lost notebook

Authors: Jaebum Sohn Sung Geun Lim Soon Yi Kang

Source: Journal of Mathematical Analysis and Applications. 307:153-166

Subject Terms: Orthogonal polynomials, Hamburger moment problems, Continued fractions, Applied Mathematics, 05 social sciences, Integration, transformation formulas, continued fractions, Other special orthogonal polynomials and functions, Hypergeometric functions, 01 natural sciences, Other hypergeometric functions and integrals in several variables, Moment problems, Stieltjes transform, 0101 mathematics, integral formulas, orthogonal polynomials, 0503 education, Analysis, hypergeometric functions

File Description: application/xml

Access URL: https://zbmath.org/2174930
https://doi.org/10.1016/j.jmaa.2004.12.054
https://core.ac.uk/display/82276447
https://www.sciencedirect.com/science/article/abs/pii/S0022247X04010741
https://www.sciencedirect.com/science/article/pii/S0022247X04010741
http://ui.adsabs.harvard.edu/abs/2005JMAA..307..153K/abstract
https://yonsei.pure.elsevier.com/en/publications/the-continuous-symmetric-hahn-polynomials-found-in-ramanujans-los

A unified inverse Laplace transform formula involving the product of a general class of polynomials and the Fox $H$-function: A unified inverse Laplace transform formula involving the product of a general class of polynomials and the Fox \(H\)-function

Authors: Deepika Singh R. C. Soni

Source: Tamkang Journal of Mathematics. 36:87-92

Subject Terms: Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Other hypergeometric functions and integrals in several variables, Hermite polynomials, Laplace transform, Hypergeometric integrals and functions defined by them (\(E\), \(G\), \(H\) and \(I\) functions), Integral transforms of special functions, inverse Laplace transform, general polynomial, Fox \(H\)-function, Laguerre polynomials, modified Bessel function, 0101 mathematics, 01 natural sciences

File Description: application/xml

Access URL: https://journals.math.tku.edu.tw/index.php/TKJM/article/download/120/131
https://zbmath.org/2220060
http://journals.math.tku.edu.tw/index.php/TKJM/article/view/120/0

Homological methods for hypergeometric families

Authors: Uli Walther Ezra Miller Laura Felicia Matusevich

Source: Journal of the American Mathematical Society. 18:919-941

Subject Terms: hypergeometric system, holomorphic D-module, semigroup ring, Determinantal varieties, Mathematics - Commutative Algebra, Commutative Algebra (math.AC), 01 natural sciences, Other hypergeometric functions and integrals in several variables, Mathematics - Algebraic Geometry, Commutative rings of differential operators and their modules, Local cohomology and commutative rings, FOS: Mathematics, 0101 mathematics, Algebraic Geometry (math.AG)

File Description: application/xml

Access URL: https://www.ams.org/jams/2005-18-04/S0894-0347-05-00488-1/S0894-0347-05-00488-1.pdf
http://arxiv.org/abs/math/0406383
https://zbmath.org/2199897
https://doi.org/10.1090/s0894-0347-05-00488-1
https://www.jstor.org/stable/20161262
https://www.ams.org/journals/jams/2005-18-04/S0894-0347-05-00488-1/home.html
https://www.arxiv-vanity.com/papers/math/0406383/
https://www.ams.org/jams/2005-18-04/S0894-0347-05-00488-1/S0894-0347-05-00488-1.pdf

Noncommutative Hypergeometry: Noncommutative hypergeometry

Authors: Volkov, Alexandre Theoretical Physics

Contributors: Volkov, Alexandre Theoretical Physics

Source: Communications in Mathematical Physics. 258:257-273

Subject Terms: Geometry of quantum groups, Other hypergeometric functions and integrals in several variables, double sine, Euler's Gamma function, \(\gamma \)-function, Mathematics - Quantum Algebra, 0103 physical sciences, FOS: Mathematics, Quantum Algebra (math.QA), Groups and algebras in quantum theory and relations with integrable systems, noncompact quantum dilogarithm, 0101 mathematics, 01 natural sciences

File Description: application/xml

Access URL: http://arxiv.org/pdf/math/0312084
http://arxiv.org/abs/math/0312084
https://arxiv.org/pdf/math/0312084
https://arxiv.org/abs/math/0312084
https://biblio.vub.ac.be/vubir/noncommutative-hypergeometry(c28e6101-66e3-489a-8027-860b1ca6098f).html

Balanced Configurations of 2n + 1 Plane Vectors: Balanced configurations of \(2 n + 1\) plane vectors

Authors: N. Ressayre

Source: Journal of Algebraic Combinatorics. 21:281-287

Subject Terms: regular plane polygons, Basic linear algebra, Mathematics - Rings and Algebras, 0102 computer and information sciences, 01 natural sciences, Other hypergeometric functions and integrals in several variables, Mathematics - Algebraic Geometry, Rings and Algebras (math.RA), FOS: Mathematics, Mathematics - Combinatorics, Symmetry properties of polytopes, Combinatorics (math.CO), 0101 mathematics, Algebraic Geometry (math.AG)

File Description: application/xml

Access URL: https://link.springer.com/content/pdf/10.1007%2Fs10801-005-6912-2.pdf
http://arxiv.org/abs/math/0206234
https://hal.archives-ouvertes.fr/hal-00122680
https://link.springer.com/article/10.1007/s10801-005-6912-2
https://paperity.org/p/6203643/balanced-configurations-of-2n-1-plane-vectors
https://link.springer.com/content/pdf/10.1007%2Fs10801-005-6912-2.pdf

Singularities of hypergeometric functions in several variables

Authors: Mikael Passare A. K. Tsikh Timur Sadykov

Source: Compositio Mathematica. 141:787-810

Subject Terms: nonconfluency, discriminant, supports, Bergman kernels of complex ellipsoidal domains, Ore-Sato coefficient, Gauss equation, vector differential operator, toric geometry, 01 natural sciences, hypergeometric series, fan, two-sided Abel lemma, Other hypergeometric functions and integrals in several variables, amoebas, Puiseux series solution to the Horn hypergeometric system, meromorphic nonconfluent hypergeometric functions, 0101 mathematics, Newton polytopes, Gelfand-Kapranov-Zelevinskij system, minimality, singularities of nonconfluent hypergeometric functions

File Description: application/xml

Access URL: https://zbmath.org/2183041
https://doi.org/10.1112/s0010437x04001411
https://www.cambridge.org/core/services/aop-cambridge-core/content/view/8BCF4C3A8644C42F3569E83EDCA90E1C/S0010437X04001411a.pdf/div-class-title-singularities-of-hypergeometric-functions-in-several-variables-div.pdf
https://pure.mpg.de/pubman/faces/ViewItemOverviewPage.jsp?itemId=item_3124455
https://www.cambridge.org/core/journals/compositio-mathematica/article/singularities-of-hypergeometric-functions-in-several-variables/8BCF4C3A8644C42F3569E83EDCA90E1C
http://journals.cambridge.org/abstract_S0010437X04001411

Identities for Hypergeometric Integrals of Different Dimensions: Identities for hypergeometric integrals of different dimensions

Authors: Alexander Varchenko Vitaly Tarasov

Source: Letters in Mathematical Physics. 71:89-99

Subject Terms: hypergeometric integrals, Knizhnik-Zamolodchikov equations, Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations, FOS: Physical sciences, Connections of hypergeometric functions with groups and algebras, and related topics, Mathematical Physics (math-ph), 01 natural sciences, Other hypergeometric functions and integrals in several variables, Mathematics - Quantum Algebra, 0103 physical sciences, FOS: Mathematics, Quantum Algebra (math.QA), Representation Theory (math.RT), 0101 mathematics, Mathematical Physics, Mathematics - Representation Theory

File Description: application/xml

Access URL: http://arxiv.org/pdf/math/0305224
http://arxiv.org/abs/math/0305224
https://zbmath.org/2168123
https://doi.org/10.1007/s11005-004-6364-y
https://ui.adsabs.harvard.edu/abs/2005LMaPh..71...89T/abstract
https://link.springer.com/content/pdf/10.1007/s11005-004-6364-y.pdf
https://rd.springer.com/article/10.1007/s11005-004-6364-y
https://link.springer.com/article/10.1007/s11005-004-6364-y

A GENERALIZATION OF THE BETA INTEGRAL ARISING FROM THE KNIZHNIK-ZAMOLODCHIKOV EQUATION FOR THE VECTOR REPRESENTATIONS OF TYPES Bn, Cn AND Dn: A generalization of the beta integral arising from the Knizhnik-Zamolodchikov equation for the vector representations of types \(B_n\), \(C_n\) and \(D_n\)

Authors: K. Mimachi T.Takamuki

Source: Kyushu Journal of Mathematics. 59:117-126

Subject Terms: Other hypergeometric functions and integrals in several variables, 4. Education, Beta integral, 0101 mathematics, 16. Peace & justice, Knizhnik-Zamolodchikov equation, Selberg integral, 01 natural sciences, Two-dimensional field theories, conformal field theories, etc. in quantum mechanics

File Description: application/xml

Access URL: https://www.jstage.jst.go.jp/article/kyushujm/59/1/59_1_117/_pdf
https://zbmath.org/2186554
https://doi.org/10.2206/kyushujm.59.117
http://catalog.lib.kyushu-u.ac.jp/en/recordID/11723

Hypergeometric functions over an arbitrary field: Hypergeometric functions over an arbitrary field.

Authors: Vladimir Retakh Mark Iosifovich Graev I M Gel'fand

Source: Russian Mathematical Surveys. 59:831-905

Subject Terms: Other hypergeometric functions and integrals in several variables, Special functions in characteristic \(p\) (gamma functions, etc.), hypergeometric function locally compact field, 0102 computer and information sciences, 0101 mathematics, 01 natural sciences, Mellin transform

File Description: application/xml

Access URL: https://zbmath.org/2170107
https://doi.org/10.1070/rm2004v059n05abeh000771
http://ui.adsabs.harvard.edu/abs/2004RuMaS..59R...2G/abstract
https://iopscience.iop.org/article/10.1070/RM2004v059n05ABEH000771

A SUMMATION FORMULA OF6F5(1): A summation formula of \(_ 6F_ 5(1)\).

Authors: Shaloo Malani Arjun K. Rathie Junesang Choi

Source: Communications of the Korean Mathematical Society. 19:775-778

Subject Terms: Other hypergeometric functions and integrals in several variables, Appell, Horn and Lauricella functions, 0102 computer and information sciences, 0101 mathematics, 01 natural sciences

File Description: application/xml

Access URL: http://society.kisti.re.kr/sv/SV_svpsbs03V.do?method=download&cn1=JAKO200413842030341
http://www.koreascience.or.kr/article/ArticleFullRecord.jsp?cn=DBSHCJ_2004_v19n4_775
https://www.kci.go.kr/kciportal/ci/sereArticleSearch/ciSereArtiView.kci?sereArticleSearchBean.artiId=ART000927722