Results 31 to 40 of about 2,985,600 (100)
A characterization of the Rogers q‐hermite polynomials
International Journal of Mathematics and Mathematical Sciences, Volume 18, Issue 4, Page 641-647, 1995., 1994 In this paper we characterize the Rogers q‐Hermite polynomials as the only orthogonal polynomial set which is also 𝒟q‐Appell where 𝒟q is the Askey‐Wilson finite difference operator.
Waleed A. Al-Salam
wiley +1 more source
Askey-Wilson braid algebra and centralizer of $U_q(\mathfrak{sl}_2)$ [PDF]
, 2022 A presentation of the centralizer of the three-fold tensor product of the spin $s$ representation of the quantum group $U_q(\mathfrak{sl}_2)$ is provided. It is expressed as a quotient of the Askey-Wilson braid algebra.
d'Andecy, Loic Poulain +8 more
core +1 more source
A Whittaker-Shannon-Kotelnikov sampling theorem related to the Askey-Wilson functions [PDF]
Journal of Nonlinear Mathematical Physics, 2007 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire +1 more source
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
doaj +1 more source
On First type characterizations of Askey-Wilson polynomials [PDF]
, 2023 In this chapter we characterize Askey-Wilson polynomials including specific and limiting cases of them by some structure relations of the first type.Comment: arXiv admin note: text overlap with arXiv:2301 ...
Mbouna, D., Suzuki, A.
core +1 more source
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
doaj +1 more source
An Expansion Formula for the Askey–Wilson Function [PDF]
, 2002 The Askey–Wilson function transform is a q-analogue of the Jacobi function transform with kernel given by an explicit non-polynomial eigenfunction of the Askey–Wilson second order q-difference operator. The kernel is called the Askey–Wilson function.
Stokman, Jasper V., Stokman, J.V.
core +1 more source
, 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. +1 more
core +2 more sources
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
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
core +1 more source