Results 31 to 40 of about 3,132,788 (112)
An Askey-Wilson Algebra of Rank 2
, 2023 An algebra is introduced which can be considered as a rank 2 extension of the Askey–Wilson algebra. Relations in this algebra are motivated by relations between coproducts of twisted primitive elements in the two-fold tensor product of the quantum ...
Groenevelt, W.G.M. (author) +6 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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MOMENTS OF ASKEY-WILSON POLYNOMIALS [PDF]
, 2013 New formulas for the $n^{\mathrm{th}}$ moment $\mu_n(a,b,c,d;q)$ of the Askey-Wilson polynomials are given. These are derived using analytic techniques, and by considering three combinatorial models for the moments: Motzkin paths, matchings, and ...
Stanton, Dennis +3 more
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Double Affine Hecke Algebras of Rank 1 and the Z_3-Symmetric Askey-Wilson Relations
Symmetry, Integrability and Geometry: Methods and Applications, 2010 We consider the double affine Hecke algebra H=H(k_0,k_1,k_0^v,k_1^v;q) associated with the root system (C_1^v,C_1). We display three elements x, y, z in H that satisfy essentially the Z_3-symmetric Askey-Wilson relations.
Paul Terwilliger, Tatsuro Ito
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Tridiagonal pairs and the Askey–Wilson relations
Linear Algebra and its Applications, 2005 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire +2 more sources
, 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 ...
Koornwinder, T.H.; id_orcid
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Continuous −1$-1$ hypergeometric orthogonal polynomials
Studies in Applied Mathematics, Volume 153, Issue 3, October 2024.Abstract The study of −1$-1$ orthogonal polynomials viewed as q→−1$q\rightarrow -1$ limits of the q$q$‐orthogonal polynomials is pursued. This paper presents the continuous polynomials part of the −1$-1$ analog of the q$q$‐Askey scheme. A compendium of the properties of all the continuous −1$-1$ hypergeometric polynomials and their connections is ...
Jonathan Pelletier +2 more
wiley +1 more source
Quasi-Linear Algebras and Integrability (the Heisenberg Picture)
Symmetry, Integrability and Geometry: Methods and Applications, 2008 We study Poisson and operator algebras with the ''quasi-linear property'' from the Heisenberg picture point of view. This means that there exists a set of one-parameter groups yielding an explicit expression of dynamical variables (operators) as ...
Alexei Zhedanov, Luc Vinet
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The Universal Askey-Wilson Algebra and the Equitable Presentation of U_q(sl_2)
Symmetry, Integrability and Geometry: Methods and Applications, 2011 Around 1992 A. Zhedanov introduced the Askey-Wilson algebra AW(3). Recently we introduced a central extension Δ of AW(3) called the universal Askey-Wilson algebra. In this paper we discuss a connection between Δ and the quantum algebra U_q(sl_2).
Paul Terwilliger
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A Polynomial Blossom for the Askey–Wilson Operator
, 2018 We introduce a blossoming procedure for polynomials related to the Askey–Wilson operator. This new blossom is symmetric, multiaffine, and reduces to the complex representation of the polynomial on a certain diagonal. This Askey–Wilson blossom can be used
Goldman, Ron, Simeonov, Plamen
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