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Befriending Askey–Wilson polynomials [PDF]
Infinite Dimensional Analysis, Quantum Probability and Related Topics, 2014 We recall five families of polynomials constituting a part of the so-called Askey–Wilson scheme. We do this to expose properties of the Askey–Wilson (AW) polynomials that constitute the last, most complicated element of this scheme. In doing so we express AW density as a product of the density that makes q-Hermite polynomials orthogonal times a ...
Paweł J. Szabłowski
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A projection formula for the Askey-Wilson polynomials and an application [PDF]
Proceedings of the American Mathematical Society, 1988 A projection formula for p n ( x ; a , b , c , d | q ) {p_n}(x;a,b,c,d|q) , the Askey-Wilson polynomials, is obtained by using a generalization of Askey and Wilson’s q q
Mizan Rahman
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On the Askey-Wilson and Rogers Polynomials [PDF]
Canadian Journal of Mathematics, 1988 The q-shifted factorial (a)n or (a; q)n isand an empty product is interpreted as 1. Recently, Askey and Wilson [6] introduced the polynomials1.1where1.2and1.3We shall refer to these polynomials as the Askey-Wilson polynomials or the orthogonal 4ϕ3 polynomials. They generalize the 6 — j symbols and are the most general classical orthogonal polynomials, [
Mourad E. H. Ismail, Dennis Stanton
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On Another Characterization of Askey-Wilson Polynomials [PDF]
Results in Mathematics, 2022 In this paper we show that the only sequences of orthogonal polynomials $(P_n)_{n\geq 0}$ satisfying \begin{align*} ϕ(x)\mathcal{D}_q P_{n}(x)=a_n\mathcal{S}_q P_{n+1}(x) +b_n\mathcal{S}_q P_n(x) +c_n\mathcal{S}_q P_{n-1}(x), \end{align*} ($c_n\neq 0$) where $ϕ$ is a well chosen polynomial of degree at most two, $\mathcal{D}_q$ is the Askey-Wilson ...
D. Mbouna, A. Suzuki
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Turán Inequalities for Symmetric Askey-Wilson Polynomials [PDF]
Rocky Mountain Journal of Mathematics, 2000 The authors study a renormalized \(A-W\) polynomial \(V_n(x)\). Using the Szász technique they establish the inequalities \[ 0\leq V_n^2(x)-V_{n+1} (x)V_{n-1} (x)\leq K, \] where \(K\) is independent of \(x\). The two inequalities hold under certain conditions upon parameters and variable.
Luís Daniel Abreu, J. Bustoz
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The associated Askey-Wilson polynomials [PDF]
Transactions of the American Mathematical Society, 1991 The most general system of basic hypergeometric orthogonal polynomials are the Askey-Wilson polynomials, which are given as a basic hypergeometric series \(_ 4\Phi_ 3\). Like all orthogonal polynomials they satisfy a three-term recurrence relation \[ 2xp_ n(x)=A_ np_{n+1}(x)+B_ np_ n(x)+C_ np_{n-1}(x). \] The recurrence coefficients \(A_ n\), \(B_ n\),
Mourad E. H. Ismail, Mizan Rahman
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Proof of two conjectures on Askey-Wilson polynomials
Proceedings of the American Mathematical Society, 2023 We give positive answer to two conjectures posed by M. E. H Ismail in his monograph [Classical and quantum orthogonal polynomials in one variable, Cambridge University Press, Cambridge, 2005]. These results generalize the classical problems of Sonine and Hahn.
K. Castillo, D. Mbouna
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Scholarpedia, 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 cases.
Tom H. Koornwinder
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The factorization method for the Askey-Wilson polynomials.
Journal of Computational and Applied Mathematics, 1998 A special Infeld-Hall factorization is given for the Askey-Wilson second order q-difference operator. It is then shown how to deducd a generalization of the corresponding Askey-Wilson polynomials.
Gaspard Bangerezako
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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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