Search Results - Nonterminating basic hypergeometric functions

Product formulas for basic hypergeometric series by evaluations of Askey--Wilson polynomials

Authors: Cohl, Howard Schlosser, Michael

Subject Terms: Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics

Access URL: http://arxiv.org/abs/2411.03571

Nonterminating transformations and summations associated with some q-Mellin–Barnes integrals.

Authors: Cohl, Howard S. Costas-Santos, Roberto S.

Source: Advances in Applied Mathematics. Jun2023, Vol. 147, pN.PAG-N.PAG. 1p.

Subject Terms: *HYPERGEOMETRIC series, *THETA functions, *HYPERGEOMETRIC functions, *INTEGRALS, *INTEGRAL representations

A Q-Sampling Theorem and Product Formula for Continuous Q-Jacobi Functions

Authors: Bouzeffour, Fethi

Source: Proceedings of the American Mathematical Society, 2007 Jul 01. 135(7), 2131-2139.

Access URL: http://dx.doi.org/10.1090/S0002-9939-07-08717-5

ABEL'S METHOD ON SUMMATION BY PARTS AND BILATERAL WELL-POISED 4Ψ4-SERIES IDENTITIES.

Authors: Chu Wenchang¹ chu.wenchang@unile.it

Source: Journal of Concrete & Applicable Mathematics. Oct2008, Vol. 6 Issue 4, p403-416. 14p.

Subject Terms: Abel integral equations, Hypergeometric series, Mathematical analysis, Hypergeometric functions, Stochastic convergence

New Infinite Families of Exact Sums of Squares Formulas, Jacobi Elliptic Functions, and Ramanujan's Tau Function

Authors: Milne, Stephen C.

Source: Proceedings of the National Academy of Sciences of the United States of America, 1996 Dec . 93(26), 15004-15008.

Access URL: https://www.jstor.org/stable/40817

Bilateral Bailey lemma and Rogers–Ramanujan identities

Authors: Chu, Wenchang Zhang, Wenlong

Source: Advances in Applied Mathematics. Mar2009, Vol. 42 Issue 3, p358-391. 34p.

Subject Terms: *TRANSFORMATION groups, *UNILATERAL disarmament, *HYPERGEOMETRIC functions, *TRANSCENDENTAL functions

Utility of integral representations for basic hypergeometric functions and orthogonal polynomials

Authors: Howard S. Cohl Roberto S. Costas-Santos

Source: The Ramanujan Journal. 61:649-674

Subject Terms: Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, 33D15, 33D60, 0101 mathematics, 01 natural sciences

Access URL: http://arxiv.org/abs/2108.03275

Some Summation Formulae for Nonterminating Basic Hypergeometric Series: Some summation formulae for nonterminating basic hypergeometric series

Authors: V. K. Jain A. Verma

Source: SIAM Journal on Mathematical Analysis. 16:647-655

Subject Terms: Cayley-Orr type formulas, Basic hypergeometric functions in one variable, \({}_r\phi_s\), basic hypergeometric series, 0102 computer and information sciences, 0101 mathematics, 01 natural sciences

File Description: application/xml

Access URL: https://epubs.siam.org/doi/10.1137/0516048
https://locus.siam.org/doi/abs/10.1137/0516048

A nonterminating 8φ7 summation for the root system Cr: A nonterminating \(_8\phi_7\) summation for the root system \(C_r\).

Authors: Michael J. Schlosser

Source: Journal of Computational and Applied Mathematics. 160:283-296

Subject Terms: 1010 Mathematics, 1010 Mathematik, multiple \(q\)-integrals, \(q\)-series, q-series, 01 natural sciences, Nonterminating 3φ2 summation, root system \(C_r\), Cr series, \(q\)-gamma functions, \(q\)-beta functions and integrals, Mathematics - Quantum Algebra, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Sp(r) series, Quantum Algebra (math.QA), 0101 mathematics, Ar series, Basic hypergeometric functions associated with root systems, U(n) series, Applied Mathematics, determinant method, Computational Mathematics, Nonterminating 8φ7 summation, nonterminating \(_8\phi_7\) summation, Mathematics - Classical Analysis and ODEs, Multiple q-integrals, 33D67 (Primary) 05A30, 33D05 (Secondary)

File Description: application/xml

Access URL: http://arxiv.org/abs/math/0211151
https://zbmath.org/2006435
https://doi.org/10.1016/s0377-0427(03)00632-0
http://arxiv.org/pdf/math/0211151.pdf
https://arxiv.org/abs/math/0211151
https://www.sciencedirect.com/science/article/abs/pii/S0377042703006320
https://www.sciencedirect.com/science/article/pii/S0377042703006320
https://ui.adsabs.harvard.edu/abs/2003JCoAM.160..283S/abstract

Invariance groups of transformations of basic hypergeometric series

Authors: K. Srinivasa Rao J. Van der Jeugt

Source: Journal of Mathematical Physics. 40:6692-6700

Subject Terms: invariance groups, transformation formulas, basic hypergeometric series, 0101 mathematics, Connections of basic hypergeometric functions with quantum groups, Chevalley groups, \(p\)-adic groups, Hecke algebras, and related topics, 01 natural sciences

File Description: application/xml

Access URL: https://core.ac.uk/display/55782148
https://biblio.ugent.be/publication/111506
https://ui.adsabs.harvard.edu/abs/1999JMP....40.6692V/abstract
https://aip.scitation.org/doi/10.1063/1.533115

The $q$ and $q^{-1}$-symmetric orthogonal polynomials in the $q$-Askey scheme, their dual polynomials and functions, orthogonality, generating functions and relations and nonterminating $q$-Chaundy double product representations

Authors: Cohl, Howard S. Costas-Santos, Roberto S.

Subject Terms: 33D45, 05A15, 42C05, 33D15, Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics

Access URL: http://arxiv.org/abs/2307.04884

Summations and transformations for multiple basic and elliptic hypergeometric series by determinant evaluations

Authors: Michael J. Schlosser Hjalmar Rosengren

Source: Indagationes Mathematicae. 14:483-513

Subject Terms: 1010 Mathematics, Mathematics(all), 1010 Mathematik, basic hypergeometric series, 01 natural sciences, \(q\)-gamma functions, \(q\)-beta functions and integrals, Mathematics - Classical Analysis and ODEs, Mathematics - Quantum Algebra, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Mathematics - Combinatorics, Quantum Algebra (math.QA), Combinatorics (math.CO), 33D67 (Primary) 05A30, 33D05 (Secondary), 0101 mathematics, Basic hypergeometric functions associated with root systems

File Description: application/xml

Access URL: http://arxiv.org/abs/math/0304249
https://zbmath.org/2077016
https://doi.org/10.1016/s0019-3577(03)90058-9
https://ucrisportal.univie.ac.at/de/publications/d803c47c-5ec9-4121-9077-521d66aca8b2
https://research.chalmers.se/en/publication/102509
https://www.sciencedirect.com/science/article/pii/S0019357703900589
https://www.arxiv-vanity.com/papers/math/0304249/
https://www.sciencedirect.com/science/article/abs/pii/S0019357703900589

Some Orthogonal Very-Well-Poised 8ϕ7-Functions that Generalize Askey–Wilson Polynomials: Some orthogonal very-well-poised \(_8\varphi_7\)-functions that generalize Askey-Wilson polynomials

Authors: Sergei K. Suslov

Source: The Ramanujan Journal. 5:183-218

Subject Terms: Sturm-Liouville theory, Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.), Basic hypergeometric functions in one variable, \({}_r\phi_s\), Mathematics - Classical Analysis and ODEs, 4. Education, orthogonal functions, Classical Analysis and ODEs (math.CA), FOS: Mathematics, 0101 mathematics, Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis, 01 natural sciences, \(q\)-Bessel functions

File Description: application/xml

Access URL: http://arxiv.org/abs/math/9707213
https://zbmath.org/1688721
https://doi.org/10.1023/a:1011439924912
https://link.springer.com/article/10.1023/A:1011439924912
https://asu.pure.elsevier.com/en/publications/some-orthogonal-very-well-poised-sub8%CF%867sub-functions-that-general

A Multidimensional Generalization of Shukla's 8ψ8 Summation: A multidimensional generalization of Shukla's \(_8\psi _8\) summation

Authors: Michael J. Schlosser

Source: Constructive Approximation. 19:163-178

Subject Terms: 1010 Mathematics, 33D15, 33D67, 1010 Mathematik, \(q\)-series, basic hypergeometric series, \(U(r)\) series, \(_8\psi_8\) summation, 01 natural sciences, \(_6\phi_5\) summation, Basic hypergeometric functions in one variable, \({}_r\phi_s\), Mathematics - Classical Analysis and ODEs, \(A_r\) series, bilateral series, Mathematics - Quantum Algebra, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Mathematics - Combinatorics, Quantum Algebra (math.QA), Combinatorics (math.CO), 0101 mathematics, Basic hypergeometric functions associated with root systems

File Description: application/xml

Access URL: http://arxiv.org/pdf/math/0103024
http://arxiv.org/abs/math/0103024
https://zbmath.org/1903774
https://doi.org/10.1007/s00365-001-0016-6
https://ucrisportal.univie.ac.at/de/publications/348d34a7-2ebf-4d6f-a128-df0562ad5534
http://ui.adsabs.harvard.edu/abs/2001math......3024S/abstract
https://link.springer.com/article/10.1007/s00365-001-0016-6
https://arxiv.org/pdf/math/0103024v1

Ramanujan-type continuous measures for classicalq-polynomials: Ramanujan-type continuous measures for classical \(q\)-polynomials

Authors: Natig M. Atakishiyev

Source: Theoretical and Mathematical Physics. 105:1500-1508

Subject Terms: Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.), \(p\)-Hermite polynomials, 0103 physical sciences, Ramanujan-type measures, Applications of basic hypergeometric functions, 0101 mathematics, Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis, 01 natural sciences

File Description: application/xml

Access URL: https://zbmath.org/1120307
https://doi.org/10.1007/bf02070870
https://link.springer.com/article/10.1007/BF02070870
https://link.springer.com/content/pdf/10.1007/BF02070870.pdf
http://ui.adsabs.harvard.edu/abs/1995TMP...105.1500A/abstract

U(n) very-well-poised 10Ø9 transformations: \(U(n)\) very-well-poised \(_{10}\phi_ 9\) transformations

Authors: John W. Newcomb Stephen C. Milne

Source: Journal of Computational and Applied Mathematics. 68:239-285

Subject Terms: Applied Mathematics, root systems, U(n + 1)4Ø3 Sears transformations, basic hypergeometric series, 01 natural sciences, Very-well-poised on unitary groups U(n + 1), U(n + 1) q-Whipple transformations, U(n + 1) terminating 10Ø9 transformations, Computational Mathematics, Generalized basic hypergeometric series, U(n + 1) terminating q-Dougall summations, \(q\)-calculus and related topics, Multiple basic hypergeometric series, 0101 mathematics, Connections of basic hypergeometric functions with quantum groups, Chevalley groups, \(p\)-adic groups, Hecke algebras, and related topics, U(n + 1) classical Bailey transform, Combinatorial identities, bijective combinatorics

File Description: application/xml

Access URL: https://www.sciencedirect.com/science/article/pii/0377042795002480
https://core.ac.uk/display/81180392

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

File Description: application/xml

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

Ramanujan-type continuous measures for classical q-polynomials.

Authors: Atakishiyev, N.

Source: Theoretical & Mathematical Physics; Dec1995, Vol. 105 Issue 3, p1500-1508, 9p

Utility of integral representations for basic hypergeometric functions and orthogonal polynomials.

Authors: Cohl, Howard S. Costas-Santos, Roberto S.

Source: Ramanujan Journal; Jun2023, Vol. 61 Issue 2, p649-674, 26p

A simple proof of Bailey’s very-well-poised ₆𝜓₆ summation: A simple proof of Bailey's very-well-poised \({}_{6}\psi_{6}\) summation

Authors: Michael J. Schlosser

Source: Proceedings of the American Mathematical Society. 130:1113-1123

Subject Terms: 1010 Mathematics, 1010 Mathematik, 33D15, 0102 computer and information sciences, 01 natural sciences, Basic hypergeometric functions in one variable, \({}_r\phi_s\), Mathematics - Classical Analysis and ODEs, Mathematics - Quantum Algebra, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Mathematics - Combinatorics, Quantum Algebra (math.QA), Combinatorics (math.CO), 0101 mathematics, very-well-poised series

File Description: application/xml

Access URL: https://www.ams.org/proc/2002-130-04/S0002-9939-01-06175-5/S0002-9939-01-06175-5.pdf
http://arxiv.org/abs/math/0007046
https://documat.unirioja.es/servlet/articulo?codigo=674796
https://ui.adsabs.harvard.edu/abs/2000math......7046S/abstract
https://www.ams.org/proc/2002-130-04/S0002-9939-01-06175-5/S0002-9939-01-06175-5.pdf
https://dialnet.unirioja.es/servlet/articulo?codigo=674796
https://www.ams.org/journals/proc/2002-130-04/S0002-9939-01-06175-5/home.html
https://arxiv.org/pdf/math/0007046.pdf
https://arxiv.org/abs/math/0007046