Search Results - Other hypergeometric functions and integrals in several variables*

Two New Degenerate Hypergeometric Functions of Several Variables and Integral Equations Containing These Functions: Two new degenerate hypergeometric functions of several variables and integral equations containing these functions

Authors: V. I. Khudozhnikov

Source: Differential Equations. 39:881-891

Subject Terms: Other hypergeometric functions and integrals in several variables, Appell, Horn and Lauricella functions, Volterra integral equations, 0103 physical sciences, 0101 mathematics, 01 natural sciences, hypergeometric functions, Lauricella functions

File Description: application/xml

Access URL: https://link.springer.com/article/10.1023/B%3ADIEQ.0000008415.44977.30

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

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

Fractional Derivatives of Certain Generalized Hypergeometric Functions of Several Variables: Fractional derivatives of certain generalized hypergeometric functions of several variables

Authors: P.K. Vishwakarma Hari M. Srivastava R.C.S. Chandel

Source: Journal of Mathematical Analysis and Applications. 184:560-572

Subject Terms: multivariable \(H\)-function, Other hypergeometric functions and integrals in several variables, Fractional derivatives and integrals, Applied Mathematics, Integral transforms of special functions, 0101 mathematics, 01 natural sciences, Analysis

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Access URL: https://zbmath.org/635945
https://doi.org/10.1006/jmaa.1994.1221
https://core.ac.uk/display/82207870
https://www.sciencedirect.com/science/article/abs/pii/S0022247X84712212#!
https://www.sciencedirect.com/science/article/pii/S0022247X84712212

A Class of Generalized Hypergeometric Functions in Several Variables: A class of generalized hypergeometric functions in several variables

Authors: Zhi Min Yan

Source: Canadian Journal of Mathematics. 44:1317-1338

Subject Terms: Other hypergeometric functions and integrals in several variables, Hypergeometric integrals and functions defined by them (\(E\), \(G\), \(H\) and \(I\) functions), Jack polynomials, 0101 mathematics, 16. Peace & justice, 01 natural sciences

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Access URL: https://www.cambridge.org/core/journals/canadian-journal-of-mathematics/article/class-of-generalized-hypergeometric-functions-in-several-variables/6084B18E34F0DD000F3491A4E48A03AA

The integral analogue of the Leibniz rule for fractional calculus and its applications involving functions of several variables

Authors: N. Shrivastava B.B. Jaimini Hari M. Srivastava

Source: Computers & Mathematics with Applications. 41:149-155

Subject Terms: Infinite integrals, Fractional calculus, Leibniz rule, fractional calculus, 01 natural sciences, Multivariable hypergeometric functions, Lauricella functions, Other hypergeometric functions and integrals in several variables, Computational Mathematics, Appell, Horn and Lauricella functions, Computational Theory and Mathematics, Fractional derivatives and integrals, Modelling and Simulation, infinite integrals, (Srivastava-Daoust) Generalized Lauricella function, multivariable hypergeometric functions, 0101 mathematics, generalized Lauricella function

File Description: application/xml

Access URL: https://zbmath.org/1671923
https://doi.org/10.1016/s0898-1221(01)85013-6
https://www.sciencedirect.com/science/article/pii/S0898122101850136

An integral equation involving the confluent hypergeometric function of several complex variables†: An integral equation involving the confluent hypergeometric function of several complex variables

Authors: H. M. Srivastava

Source: Applicable Analysis. 5:251-256

Subject Terms: Other hypergeometric functions and integrals in several variables, 0101 mathematics, Integral equations with miscellaneous special kernels, 01 natural sciences

File Description: application/xml

Access URL: https://zbmath.org/3359135
https://www.tandfonline.com/doi/full/10.1080/00036817608839128

A Study To Investigate One-Variable Feyman Diagrams Based On Differential Reduction Of Hypergeometric Functions.

Authors: Xing Kongduo Midhunchakkaravarthy

Source: Frontiers in Health Informatics; 2024, Vol. 13 Issue 8, p5207-5213, 7p

Subject Terms: MATHEMATICAL transformations, QUANTUM field theory, FEYNMAN integrals, SCATTERING amplitude (Physics), MATHEMATICAL physics

A Study To Examine Single-Variable Feyman Diagrams Utilising Differential Reduction Of Hypergeometric Functions.

Authors: Xing Kongduo Midhunchakkaravarthy

Source: Frontiers in Health Informatics; 2024, Vol. 13 Issue 8, p5165-5171, 7p

Subject Terms: MATHEMATICAL transformations, QUANTUM field theory, FEYNMAN integrals, SCATTERING amplitude (Physics), MATHEMATICAL physics

Fractional integration of the H-function of several variables: Fractional integration of the \(H\)-function of several variables

Authors: Mudhir A. Abdul Hussain Hari M. Srivastava

Source: Computers & Mathematics with Applications. 30:73-85

Subject Terms: multivariable \(H\)-function, Hypergeometric integrals and functions defined by them (\(E\), \(G\), \(H\) and \(I\) functions), H-functions of one and more variables, Fractional calculus, 01 natural sciences, Eulerian integrals, (Srivastava-Daoust) generalized Lauricella function, Other hypergeometric functions and integrals in several variables, Computational Mathematics, Fractional integration, Computational Theory and Mathematics, Fractional derivatives and integrals, Modelling and Simulation, Gamma and Beta functions, Appell functions, fractional integration, 0101 mathematics, Mellin-Barnes contour integrals, Binomial expansion

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Access URL: https://zbmath.org/820326
https://doi.org/10.1016/0898-1221(95)00148-r
https://dspace.library.uvic.ca/handle/1828/2602
https://www.sciencedirect.com/science/article/pii/089812219500148R

Generalized Euler integrals and A-hypergeometric functions: Generalized Euler integrals and \(A\)-hypergeometric functions

Authors: M. M. Kapranov Andrei Zelevinsky Gel'fand Im

Source: Advances in Mathematics. 84:255-271

Subject Terms: Other hypergeometric functions and integrals in several variables, Mathematics(all), 0103 physical sciences, integral representations, \(A\)-hypergeometric functions, generalized Euler integral, 0101 mathematics, 01 natural sciences, \(A\)-hypergeometric system

File Description: application/xml

Access URL: https://www.sciencedirect.com/science/article/abs/pii/000187089090048R
https://www.sciencedirect.com/science/article/pii/000187089090048R

Some integral representations of multivariable hypergeometric functions

Authors: Vu Kim Tuan Megumi Saigo

Source: Rendiconti del Circolo Matematico di Palermo. 41:69-80

Subject Terms: hypergeometric functions in several variables, Gauss function, Integral transforms of special functions, multiple integral representations, 02 engineering and technology, Kampé de Fériet function, Lauricella functions, Other hypergeometric functions and integrals in several variables, Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.), 0203 mechanical engineering, Kummer function, modified Bessel functions, 0202 electrical engineering, electronic engineering, information engineering, Special integral transforms (Legendre, Hilbert, etc.), Mellin transformation

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Access URL: https://zbmath.org/91667
https://doi.org/10.1007/bf02844464
https://link.springer.com/article/10.1007/BF02844464

On a hypergeometric function of four variables with a new aspect ofSL-symmetry: On a hypergeometric function of four variables with a new aspect of \(SL\)- symmetry

Authors: Harold Exton

Source: Annali di Matematica Pura ed Applicata (1923 -). 161:315-343

Subject Terms: Other hypergeometric functions and integrals in several variables, hypergeometric PDE's, 0103 physical sciences, bisingularities for PDE's, 0101 mathematics, 01 natural sciences

File Description: application/xml

Access URL: https://zbmath.org/95003
https://doi.org/10.1007/bf01759644
https://rd.springer.com/content/pdf/10.1007%2FBF01759644.pdf
https://link.springer.com/article/10.1007/BF01759644
https://link.springer.com/content/pdf/10.1007/BF01759644.pdf

Some transformation and reduction formulas for hypergeometric series in several variables: Certain transformation and reduction formulas for hypergeometric series in several variables

Authors: C. C. Grosjean Hari M. Srivastava

Source: Journal of Computational and Applied Mathematics. 37:287-299

Subject Terms: Other hypergeometric functions and integrals in several variables, Computational Mathematics, Appell, Horn and Lauricella functions, multiple series identities, hypergeometric transformations, Applied Mathematics

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Access URL: https://zbmath.org/1150
https://doi.org/10.1016/0377-0427(91)90125-4
https://www.sciencedirect.com/science/article/pii/0377042791901254

On hypergeometric functions in several variables II. The Wronskian of the hypergeometric functions of type (n+1,m+1): On hypergeometric functions in several variables. II: The Wronskian of the hypergeometric functions of type \((n+1,m+1)\)

Authors: KITA, Michitake

Source: J. Math. Soc. Japan 45, no. 4 (1993), 645-669

Subject Terms: Other hypergeometric functions and integrals in several variables, 33C70, 0101 mathematics, 01 natural sciences

File Description: application/xml; application/pdf

Access URL: https://zbmath.org/562716
https://doi.org/10.2969/jmsj/04540645
https://projecteuclid.org/euclid.jmsj/1227105056
https://projecteuclid.org/download/pdf_1/euclid.jmsj/1227105056
http://ci.nii.ac.jp/naid/10006413930
https://www.jstage.jst.go.jp/article/jmath1948/45/4/45_4_645/_article
http://projecteuclid.org/euclid.jmsj/1227105056

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

Transformations for a Class of Hypergeometric Functions: Transformations for a class of hypergeometric functions

Authors: S. Mudaliar

Source: Journal of Electromagnetic Waves and Applications. 14:1185-1202

Subject Terms: Other hypergeometric functions and integrals in several variables, Other functions defined by series and integrals, 0101 mathematics, Basic hypergeometric integrals and functions defined by them, Gamma, beta and polygamma functions, 01 natural sciences

File Description: application/xml

Access URL: https://zbmath.org/2128020
https://doi.org/10.1163/156939300x01111
http://www.tandfonline.com/doi/abs/10.1163/156939300X01111

$ \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

ON THE GENERALIZED GAUSS HYPERGEOMETRIC SYSTEM OF THREE VARIABLES: On the generalized Gauss hypergeometric system of three variables

Authors: Katsushige Higashi Takeshi Sasaki

Source: Kyushu Journal of Mathematics. 58:105-120

Subject Terms: Other hypergeometric functions and integrals in several variables, Pfaffian system, Jack polynomial, 0101 mathematics, generalized Gauss hypergeometric function, 01 natural sciences

File Description: application/xml

Access URL: https://www.jstage.jst.go.jp/article/kyushujm/58/1/58_1_105/_pdf

Further results on generalized hypergeometric functions

Authors: Leda Galué Shyam L. Kalla A. Al-Zamel

Source: Applied Mathematics and Computation. 136:17-25

Subject Terms: Other hypergeometric functions and integrals in several variables, hypergeometric incomplete gamma functions, recurrence formulas, 0101 mathematics, Gamma, beta and polygamma functions, 01 natural sciences

File Description: application/xml

Access URL: https://zbmath.org/1861369
https://doi.org/10.1016/s0096-3003(02)00014-0
https://dblp.uni-trier.de/db/journals/amc/amc136.html#GalueAK03
https://www.sciencedirect.com/science/article/pii/S0096300302000140
https://doi.org/10.1016/S0096-3003(02)00014-0