Search Results - Basic hypergeometric integrals and functions defined by them~

On the fractional q-integral operators involving q-analogue of Mittag-Leffler function: On the fractional \(q\)-integral operators involving \(q\)-analogue of Mittag-Leffler function

Authors: Mulugeta Dawud Ali D. L. Suthar

Source: Analysis. 44:245-251

Subject Terms: Integral operators, Fractional derivatives and integrals, \(q\)-generalized hypergeometric function, Riemann-Liouville fractional \(q\)-integral operator, \(q\)-beta function, Applications of basic hypergeometric functions, 0101 mathematics, Basic hypergeometric integrals and functions defined by them, Weyl fractional \(q\)-integral operator, Mittag-Leffler functions and generalizations, \(q\)-analogue of Mittag-Leffler function, 01 natural sciences, Kober fractional \(q\)-integral operator

File Description: application/xml

Access URL: https://zbmath.org/7912331
https://doi.org/10.1515/anly-2023-0107

q-Beta Integrals and Multivariate Basic Hypergeometric Series Associated to Root Systems of Type Am: \(q\)-beta integrals and multivariate basic hypergeometric series associated to root systems of type \(A_m\)

Authors: Medhat A. Rakha Robert A. Gustafson

Source: Annals of Combinatorics. 4:347-373

Subject Terms: Basic hypergeometric functions in one variable, \({}_r\phi_s\), 0101 mathematics, Basic hypergeometric integrals and functions defined by them, 01 natural sciences, Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.), Basic hypergeometric functions associated with root systems

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Access URL: https://zbmath.org/1587406
https://doi.org/10.1007/pl00001285
https://link.springer.com/article/10.1007/PL00001285
https://link.springer.com/10.1007/PL00001285

A Generalized Hypergeometric Function II. Asymptotics and D 4 Symmetry: A generalized hypergeometric function. II: Asymptotics and \(D_4\) symmetry

Authors: S.N.M. Ruijsenaars

Source: Communications in Mathematical Physics. 243:389-412

Subject Terms: Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.), Askey-Wilson polynomials, generalized hypergeometric function, Difference equations, scaling (\(q\)-differences), 0101 mathematics, Basic hypergeometric integrals and functions defined by them, Hypergeometric functions, analytic difference equations, 01 natural sciences

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Access URL: http://ui.adsabs.harvard.edu/abs/2003CMaPh.243..389R/abstract
https://link.springer.com/article/10.1007/s00220-003-0969-3

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

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

The $q$-twisted Cohomology and the $q$-hypergeometric Function at $|q|=1$: The \(q\)-twisted cohomology and the \(q\)-hypergeometric function at \(|q|=1\)

Authors: Yoshihiro Takeyama

Source: Publications of the Research Institute for Mathematical Sciences. 37:71-89

Subject Terms: Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.), Heine's transformations, 01 natural sciences, little \(q\)-Jacobi polynomials, \(q\)-gamma functions, \(q\)-beta functions and integrals, \(q\)-hypergeometric functions, Mathematics - Classical Analysis and ODEs, Mathematics - Quantum Algebra, 0103 physical sciences, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Quantum Algebra (math.QA), 0101 mathematics, Basic hypergeometric integrals and functions defined by them

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Access URL: http://www.ems-ph.org/journals/show_pdf.php?issn=0034-5318&vol=37&iss=1&rank=3
http://arxiv.org/abs/math/0005071
https://www.arxiv-vanity.com/papers/math/0005071/
https://ui.adsabs.harvard.edu/abs/2000math......5071T/abstract
http://ci.nii.ac.jp/naid/130003585492

Geometry of q-hypergeometric functions as a bridge between Yangians and quantum affine algebras: Geometric \(q\)-hypergeometric functions as a bridge between Yangians and quantum affine algebras

Authors: V. Tarasov Alexander Varchenko

Source: Inventiones mathematicae. 128:501-588

Subject Terms: quantum complex Grassmannians, quantum symmetric space, Askey-Wilson polynomials, Mathematics - Quantum Algebra, FOS: Mathematics, Quantum Algebra (math.QA), Quantum groups (quantized enveloping algebras) and related deformations, 0101 mathematics, Basic hypergeometric integrals and functions defined by them, Connections of basic hypergeometric functions with quantum groups, Chevalley groups, \(p\)-adic groups, Hecke algebras, and related topics, 01 natural sciences

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Access URL: http://arxiv.org/pdf/q-alg/9604011
http://arxiv.org/abs/q-alg/9604011
https://core.ac.uk/display/22276402
https://link.springer.com/article/10.1007%2Fs002220050151
https://ui.adsabs.harvard.edu/abs/1997InMat.128..501T/abstract
https://link.springer.com/content/pdf/10.1007/s002220050151.pdf
https://arxiv.org/abs/q-alg/9604011v4
http://export.arxiv.org/pdf/q-alg/9604011
https://arxiv.org/pdf/q-alg/9604011v4

A STUDY OF A NOVEL CATEGORY OF MACROBERT-STYLE INTEGRALS INCORPORATING GENERALIZED HYPERGEOMETRIC FUNCTIONS.

Authors: Shetty, Shwetha S. Kurumujji, Shantha Kumari Yadav, Vijay

Source: South East Asian Journal of Mathematics & Mathematical Sciences; 2025, Vol. 21 Issue 1, p149-164, 16p

Subject Terms: GENERALIZED integrals, INTEGRAL functions, GENERALIZATION, HYPERGEOMETRIC series, LITERATURE, HYPERGEOMETRIC functions

A quantum algebra approach to basic multivariable special functions

Authors: Roberto Floreanini Luc Vinet L Lapointe

Source: Journal of Physics A: Mathematical and General. 27:6781-6797

Subject Terms: 0103 physical sciences, 0101 mathematics, Basic hypergeometric integrals and functions defined by them, 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, 01 natural sciences

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Access URL: https://iopscience.iop.org/article/10.1088/0305-4470/27/20/016/meta
http://ui.adsabs.harvard.edu/abs/1994JPhA...27.6781F/abstract
https://iopscience.iop.org/article/10.1088/0305-4470/27/20/016/pdf
http://iopscience.iop.org/article/10.1088/0305-4470/27/20/016/pdf

Some relations between basic hypergeometric functions of two variables

Authors: R. P. Agarwal

Source: Rendiconti del Circolo Matematico di Palermo. 3:76-82

Subject Terms: special functions, Basic hypergeometric integrals and functions defined by them

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Access URL: https://zbmath.org/3088274
https://doi.org/10.1007/bf02849368
https://link.springer.com/article/10.1007%2FBF02849368
https://link.springer.com/content/pdf/10.1007%2FBF02849368.pdf

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

On Solutions of the q-Hypergeometric Equation with q N = 1: On solutions of the \(q\)-hypergeometric equation with \(q^N = 1\)

Authors: Yoshihiro Takeyama

Source: The Ramanujan Journal. 6:369-378

Subject Terms: \(q\)-hypergeometric equation, Basic hypergeometric functions in one variable, \({}_r\phi_s\), Mathematics - Classical Analysis and ODEs, Mathematics - Quantum Algebra, 0103 physical sciences, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Quantum Algebra (math.QA), basic hypergeometric series, root of unity, 0101 mathematics, Basic hypergeometric integrals and functions defined by them, 01 natural sciences

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Access URL: http://arxiv.org/abs/math/0106041
https://zbmath.org/1845358
https://doi.org/10.1023/a:1019785205984
https://link.springer.com/article/10.1023/A%3A1019785205984

symmetry classification for jackson integrals associated with irreducible reduced root systems: Symmetry classification for Jackson integrals associated with irreducible reduced root systems

Authors: Masahiko Ito

Source: Compositio Mathematica. 129(3):325-340

Subject Terms: Jackson integrals, Gustafson's sums, van Diejen's \(BC_n\)-sums, Aomoto's sums, elliptic product formulas, Basic hypergeometric integrals and functions defined by them, Basic hypergeometric functions associated with root systems

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Access URL: https://zbmath.org/1701638
https://doi.org/10.1023/a:1012518910847
https://www.cambridge.org/core/services/aop-cambridge-core/content/view/D1958D038A5817D9A367017E6C28D716/S0010437X01000781a.pdf/div-class-title-symmetry-classification-for-jackson-integrals-associated-with-irreducible-reduced-root-systems-div.pdf
https://www.cambridge.org/core/journals/compositio-mathematica/article/symmetry-classification-for-jackson-integrals-associated-with-irreducible-reduced-root-systems/D1958D038A5817D9A367017E6C28D716
https://link.springer.com/article/10.1023/A%3A1012518910847

q-Selberg Integrals and Macdonald Polynomials: \(q\)-Selberg integrals and Macdonald polynomials

Authors: S. Ole Warnaar

Source: The Ramanujan Journal. 10:237-268

Subject Terms: \(q\)-gamma functions, \(q\)-beta functions and integrals, Selberg integrals, symmetric functions, 0101 mathematics, Basic hypergeometric integrals and functions defined by them, 01 natural sciences, Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.)

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Access URL: http://www.maths.uq.edu.au/~uqowarna/pubs/q-Selberg.pdf
https://zbmath.org/2247912
https://doi.org/10.1007/s11139-005-4849-7
https://link.springer.com/article/10.1007/s11139-005-4849-7
https://espace.library.uq.edu.au/view/UQ:188983
https://core.ac.uk/display/15076905

On the basic hypergeometric matrix functions of two variables.

Authors: Dwivedi, Ravi Sahai, Vivek

Source: Linear & Multilinear Algebra; Jan2019, Vol. 67 Issue 1, p1-19, 19p

Subject Terms: HYPERGEOMETRIC functions, MATRIX functions, MATHEMATICAL variables, INTEGRALS, ECONOMIC convergence

A Product Formula for Jackson Integral Associated with the Root System F 4: A product formula for Jackson integral associated with the root system \(F_4\)

Authors: Masahiko Ito

Source: The Ramanujan Journal. 6:279-293

Subject Terms: Jackson integral, very-well-poised \({}_6\psi_6\) sum, Askey-Wilson integral, root system of type \(F_4\), 0101 mathematics, Basic hypergeometric integrals and functions defined by them, 01 natural sciences, Basic hypergeometric functions associated with root systems

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Access URL: https://link.springer.com/article/10.1023%2FA%3A1019711531212
https://link.springer.com/content/pdf/10.1023/A:1019711531212.pdf

On a Solution of a $q$-Difference Analogue of Laurieella's $D$-Type Hypergeometric Equation with $|q| = 1$: On a solution of a \(q\)-difference analogue of Lauricella's \(D\)-type hypergeometric equation with \(|q|=1\)

Authors: Michitomo Nishizawa

Source: Publications of the Research Institute for Mathematical Sciences. 34:277-290

Subject Terms: Lauricella's \(D\)-type hypergometric equation, Basic hypergeometric functions in one variable, \({}_r\phi_s\), 0101 mathematics, Basic hypergeometric integrals and functions defined by them, 01 natural sciences

File Description: application/xml

Access URL: http://www.ems-ph.org/journals/show_pdf.php?issn=0034-5318&vol=34&iss=3&rank=6
https://www.jstage.jst.go.jp/article/kyotoms1969/34/3/34_3_277/_article
http://ci.nii.ac.jp/naid/130003585426
https://www.ems-ph.org/journals/show_pdf.php?issn=0034-5318&vol=34&iss=3&rank=6
https://www.ems-ph.org/doi/10.2977/prims/1195144697

Biorthogonality of a System of Rational Functions with Respect to a Positive Measure on $[ - 1,1]$: Biorthogonality of a system of rational functions with respect to positive measure on \([-1,1]\)

Authors: Mizan Rahman

Source: SIAM Journal on Mathematical Analysis. 22:1430-1441

Subject Terms: Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Generalized basic hypergeometric series, q-beta integral, biorthogonality, balanced basic hypergeometric series, Basic hypergeometric integrals and functions defined by them, very well poised basic hypergeometric series

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Access URL: https://zbmath.org/24771
https://doi.org/10.1137/0522091
https://epubs.siam.org/doi/abs/10.1137/0522091

elliptic selberg integrals: Elliptic Selberg integrals

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

Source: INTERNATIONAL MATHEMATICS RESEARCH NOTICES
Artículos CONICYT
CONICYT Chile
instacron:CONICYT
Conicyt_qa
ANID
instacron:ANID
Articulos_ANID
Agencia Nacional de Investigación y Desarrollo

Subject Terms: \(q\)-gamma functions, \(q\)-beta functions and integrals, Basic hypergeometric integrals and functions defined by them, Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.)

File Description: application/xml; 2974 bytes; text/html

Access URL: http://academic.oup.com/imrn/article-abstract/2001/20/1083/847916
https://academic.oup.com/imrn/article-abstract/2001/20/1083/847916
http://hdl.handle.net/10533/173002
https://repositorio-qa.anid.cl/handle/10533/173002
https://hdl.handle.net/10533/173002

Some generating functions for the associated Askey-Wilson polynomials

Authors: Mizan Rahman

Source: Journal of Computational and Applied Mathematics. 68:287-296

Subject Terms: Computational Mathematics, Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.), Askey-Wilson and associated Askey-Wilson polynomials, Applied Mathematics, Askey-Wilson polynomial, Integral representation, Balanced well-poised and very-well-poised basic hypergeometric series, 0101 mathematics, Basic hypergeometric integrals and functions defined by them, 01 natural sciences, Generating function

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Access URL: https://www.sciencedirect.com/science/article/pii/0377042795002499
https://core.ac.uk/display/82084669
https://www.sciencedirect.com/science/article/abs/pii/0377042795002499

Differential Equations Satisfied by the Components with Respect to the Cyclic Group of Order n of Some Special Functions: Differential equations satisfied by the components with respect to the cyclic group of order \(n\) of some special functions

Authors: Youssèf Ben Cheikh

Source: Journal of Mathematical Analysis and Applications. 244:483-497

Subject Terms: Generalized hypergeometric series, \({}_pF_q\), Applied Mathematics, Linear ordinary differential equations and systems, 0101 mathematics, Basic hypergeometric integrals and functions defined by them, 01 natural sciences, Power series (including lacunary series) in one complex variable, Analysis

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Access URL: https://zbmath.org/1449219
https://doi.org/10.1006/jmaa.2000.6719
https://www.sciencedirect.com/science/article/pii/S0022247X00967192
https://core.ac.uk/display/82329563