Results 181 to 190 of about 1,056 (198)

?Hidden symmetry? of Askey-Wilson polynomials

Theoretical and Mathematical Physics, 1991
See the review in Zbl 0744.33009.
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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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On structure formulas for Wilson polynomials

Integral Transforms and Special Functions, 2015
By studying various properties of some divided difference operators, we prove that Wilson polynomials are solutions of a second-order difference equation of hypergeometric type. Next, some new structure relations are deduced, the inversion and the connection problems are solved using an algorithmic method.
P. Njionou Sadjang, W. Koepf, M. Foupouagnigni   +2 more
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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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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  

Wilson and Related Polynomials

2020
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Infinitely many shape invariant discrete quantum mechanical systems and new exceptional orthogonal polynomials related to the Wilson and Askey–Wilson polynomials

Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 2009
Satoru Odake
exaly  

The Askey–Wilson Polynomials

2005
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