Results 41 to 50 of about 3,786,908 (243)
Multiple Askey–Wilson polynomials and related basic hypergeometric multiple orthogonal polynomials [PDF]
, 2019 We first show how one can obtain Al-Salam--Chihara polynomials, continuous dual $q$-Hahn polynomials, and Askey--Wilson polynomials from the little $q$-Laguerre and the little $q$-Jacobi polynomials by using special transformations.
J. P. Nuwacu, W. Van Assche
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Askey-Wilson Polynomials and Branching Laws
Journal of Lie Theory, 2023 Connection coefficient formulas for special functions describe change of basis matrices under a parameter change, for bases formed by the special functions. Such formulas are related to branching questions in representation theory. The Askey-Wilson polynomials are one of the most general 1-variable special functions.
Back, Allen +3 more
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Multiple Wilson and Jacobi–Piñeiro polynomials
Journal of Approximation Theory, 2005 22 pages, 2 ...
Bernhard Beckermann +2 more
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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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Bispectrality of Multivariable Racah–Wilson Polynomials [PDF]
Constructive Approximation, 2009 minor ...
Geronimo, Jeffrey S., Iliev, Plamen
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Bootstrapping and Askey-Wilson polynomials [PDF]
, 2014 The mixed moments for the Askey-Wilson polynomials are found using a bootstrapping method and connection coefficients. A similar bootstrapping idea on generating functions gives a new Askey-Wilson generating function.
J. Kim, D. Stanton
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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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A characterization of the Rogers q-hermite polynomials
International Journal of Mathematics and Mathematical Sciences, 1995 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
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Recurrence Relations of the Multi-Indexed Orthogonal Polynomials : III [PDF]
, 2016 In a previous paper, we presented conjectures of the recurrence relations with constant coefficients for the multi-indexed orthogonal polynomials of Laguerre, Jacobi, Wilson and Askey-Wilson types.
Odake, Satoru
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Some transformation formulas associated with Askey-Wilson polynomials and Lassalle's formulas for Macdonald-Koornwinder polynomials [PDF]
, 2014 We present a fourfold series expansion representing the Askey-Wilson polynomials. To obtain the result, a sequential use is made of several summation and transformation formulas for the basic hypergeometric series, including the Verma's q-extension of ...
A. Hoshino, M. Noumi, J. Shiraishi
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