Results 31 to 40 of about 2,393 (108)
Advances in Mathematical Physics, Volume 2009, Issue 1, 2009., 2009 In this paper, we apply to (almost) all the “named” polynomials of the Askey scheme, as defined by their standard three‐term recursion relations, the machinery developed in previous papers. For each of these polynomials we identify at least one additional recursion relation involving a shift in some of the parameters they feature, and for several of ...
M. Bruschi +3 more
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The dynamical U(n) quantum group
International Journal of Mathematics and Mathematical Sciences, Volume 2006, Issue 1, 2006., 2006 We study the dynamical analogue of the matrix algebra M(n), constructed from a dynamical R‐matrix given by Etingof and Varchenko. A left and a right corepresentation of this algebra, which can be seen as analogues of the exterior algebra representation, are defined and this defines dynamical quantum minor determinants as the matrix elements of these ...
Erik Koelink, Yvette Van Norden
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Degenerate Sklyanin algebras, Askey–Wilson polynomials and Heun operators [PDF]
Journal of Physics A: Mathematical and Theoretical, 2020 Abstract The q-difference equation, the shift and the contiguity relations of the Askey–Wilson polynomials are cast in the framework of the three and four-dimensional degenerate Sklyanin algebras s
Julien Gaboriaud +3 more
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Multivariable q‐Hahn polynomials as coupling coefficients for quantum algebra representations
International Journal of Mathematics and Mathematical Sciences, Volume 28, Issue 6, Page 331-358, 2001., 2001 We study coupling coefficients for a multiple tensor product of highest weight representations of the SU(1, 1) quantum group. These are multivariable generalizations of the q‐Hahn polynomials.
Hjalmar Rosengren
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Orthogonal Polynomials of Askey-Wilson Type
, 2022 26 ...
Ismail, Mourad E. H. +2 more
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Orthogonal Basic Hypergeometric Laurent Polynomials
Symmetry, Integrability and Geometry: Methods and Applications, 2012 The Askey-Wilson polynomials are orthogonal polynomials in$x = cos heta$, which are given as a terminating $_4phi_3$ basic hypergeometric series. The non-symmetric Askey-Wilson polynomials are Laurent polynomials in $z=e^{iheta}$, which are given as a ...
Mourad E.H. Ismail, Dennis Stanton
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On Solutions of Holonomic Divided-Difference Equations on Nonuniform Lattices
Axioms, 2013 The main aim of this paper is the development of suitable bases that enable the direct series representation of orthogonal polynomial systems on nonuniform lattices (quadratic lattices of a discrete or a q-discrete variable). We present two bases of this
Salifou Mboutngam +3 more
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Exactly solvable `discrete' quantum mechanics; shape invariance, Heisenberg solutions, annihilation-creation operators and coherent states [PDF]
, 2008 Various examples of exactly solvable `discrete' quantum mechanics are explored explicitly with emphasis on shape invariance, Heisenberg operator solutions, annihilation-creation operators, the dynamical symmetry algebras and coherent states.
Odake, Satoru, Sasaki, Ryu
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Scholarpedia, 2012 Askey-Wilson polynomial refers to a four-parameter family of q-hypergeometric orthogonal polynomials which contains all families of classical orthogonal polynomials (in the wide sense) as special or limit cases.
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A Polynomial Blossom for the Askey–Wilson Operator [PDF]
Constructive Approximation, 2018 In this paper the authors introduce a blossoming procedure for polynomials related to the Askey-Wilson operator. This blossom is symmetric, multiaffine, and reduces to the complex representation of the polynomial on a certain diagonal. This Askey-Wilson blossom can be used to find the Askey-Wilson derivative of a polynomial of any order.
Simeonov, Plamen, Goldman, Ron
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