Results 91 to 100 of about 2,393 (108)

On a conjecture involving Askey–Wilson polynomials

Integral Transforms and Special Functions
K. Castillo, D. Mbouna
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Fourier - Gauss transforms of the Askey - Wilson polynomials

Journal of Physics A: Mathematical and General, 1997
The classical Fourier-Gauss transform can be written in the form \[ \frac{1}{\sqrt{2\pi}}\int_{-\infty}^{\infty}e^{isr-s^2/r}H_n(\sin\kappa s|q)ds =i^nq^{n^2/4}h_n(\sinh\kappa r|q)e^{-r^2/2}, \] where \(q=\exp(-2\kappa^2)\) and \(h_n(x|q)=i^{-n}H_n(ix|q^{-1})\). Here \(H_n(x|q)\) denotes the continuous \(q\)-Hermite polynomial. In [\textit{M.
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Askey-Wilson polynomials, kernel polynomials and association schemes

Graphs and Combinatorics, 1993
For many of the classical association schemes, there are specific sets of orthogonal polynomials associated with them. When these can be found explicitly, the polynomials can be given as hypergeometric or basic hypergeometric series. A new association scheme was constructed by \textit{A. A. Ivanov}, \textit{M. E. Muzichuk} and \textit{V. A. Ustimenko} [
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Nonnegative Linearization and Quadratic Transformation of Askey-Wilson Polynomials

Canadian Mathematical Bulletin, 1996
AbstractNonnegative product linearization of the Askey-Wilson polynomials is shown for a wide range of parameters. As a corollary we obtain Rahman's result on the continuous q-Jacobi polynomials with α ≥ β > — 1 and α + β + 1 ≥ 0.
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Askey-Wilson polynomials and the quantum group \(SU_ q(2)\)

1990
The Askey-Wilson polynomials are a 4-parameter family of \(q\)-orthogonal polynomials expressed by the basic hypergeometric series \({}_ 4\phi_ 3\). This article makes the observation that a (partially discrete) 4- parameter family of Askey-Wilson polynomials is realised as ``doubly associated spherical functions'' on the quantum group \(SU_ q(2 ...
Noumi, Masatoshi, Mimachi, Katsuhisa
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Associated Askey-Wilson polynomials as Laguerre-Hahn orthogonal polynomials

1988
One looks for [formal] orthogonal polynomials satisfying interesting differential or difference relations and equations (Laguerre-Hahn theory). The divided difference operator used here is essentially the Askey-Wilson operator $$Df\left( x \right) = \frac{{E_2 f\left( x \right) - E_1 f\left( x \right)}}{{E_2 x - E_1 x}} = \frac{{f\left( {y_2 \left(
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On the structure and probabilistic interpretation of Askey–Wilson densities and polynomials with complex parameters

Journal of Functional Analysis, 2011
Paweł J Szabłowski
exaly  

Asymptotics of the Wilson polynomials

Analysis and Applications, 2020
Yu-Tian Li, Xiang-Sheng Wang
exaly  

Nonsymmetric Askey–Wilson polynomials as vector-valued polynomials

Applicable Analysis, 2011
Fethi Bouzeffour
exaly  

The Askey–Wilson Polynomials

2005
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