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On the Askey-Wilson polynomials
Constructive Approximation, 1992Classical orthogonal polynomials of a discrete variable on non-uniform lattices were introduced by \textit{R. Askey} and \textit{J. A. Wilson} [SIAM J. Math. Anal. 10, 1008-1016 (1979; Zbl 0437.33014)], and \textit{J. A. Wilson} [ibid. 11, 690-701 (1980; Zbl 0454.33007)] and their main properties were established on the basis of the theory of ...
Natig M. Atakishiyev, Sergei K. Suslov
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On structure formulas for Wilson polynomials [PDF]
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 +2 more
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Asymptotics of the Wilson polynomials
Analysis and Applications, 2019In this paper, we study the asymptotic behavior of the Wilson polynomials [Formula: see text] as their degree tends to infinity. These polynomials lie on the top level of the Askey scheme of hypergeometric orthogonal polynomials. Infinite asymptotic expansions are derived for these polynomials in various cases, for instance, (i) when the variable ...
Roderick Wong +2 more
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SIAM Journal on Mathematical Analysis, 1987
Local symmetry (recurrence relation) techniques are a powerful tool for the efficient derivation of properties associated with families of hypergeometric and basic hypergeometric functions. Here these ideas are applied to the Wilson polynomials, a generalization of the classical orthogonal polynomials, to obtain the orthogonality relations and an ...
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Local symmetry (recurrence relation) techniques are a powerful tool for the efficient derivation of properties associated with families of hypergeometric and basic hypergeometric functions. Here these ideas are applied to the Wilson polynomials, a generalization of the classical orthogonal polynomials, to obtain the orthogonality relations and an ...
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Constructive Approximation, 1991
The Wilson polynomials appear on top of the Askey table of hypergeometric orthogonal polynomials and thus are, together with the Racah polynomials, the most general system of hypergeometric orthogonal polynomials. They can be written as an hypergeometric \(_ 4F_ 3(1)\) in which the variable \(x\) appears in two of the numerator parameters as the ...
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The Wilson polynomials appear on top of the Askey table of hypergeometric orthogonal polynomials and thus are, together with the Racah polynomials, the most general system of hypergeometric orthogonal polynomials. They can be written as an hypergeometric \(_ 4F_ 3(1)\) in which the variable \(x\) appears in two of the numerator parameters as the ...
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Multivariable Wilson polynomials
Journal of Mathematical Physics, 1989A multivariable biorthogonal generalization of the Wilson polynomials is presented. These are four distinct families, which in a special case occur in two complex conjugate pairs, that satisfy four biorthogonality relations among them. An interesting limit case is the multivariable continuous dual Hahn polynomials.
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?Hidden symmetry? of Askey-Wilson polynomials [PDF]
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, 1993For 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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Some Functions that Generalize the Askey-Wilson Polynomials
Communications in Mathematical Physics, 1997zbMATH Open Web Interface contents unavailable due to conflicting licenses.
F. A. Grünbaum, Luc Haine
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Fourier - Gauss transforms of the Askey - Wilson polynomials
Journal of Physics A: Mathematical and General, 1997The 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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