Results 21 to 30 of about 7,854 (155)
Bispectral commuting difference operators for multivariable Askey-Wilson polynomials [PDF]
, 2010 We construct a commutative algebra A z , generated by d algebraically independent q-difference operators acting on variables z 1 , z 2 ,..., z d , which is diagonalized by the multivariable Askey-Wilson polynomials P n (z) considered by Gasper and Rahman
Plamen Iliev
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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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Tridiagonal representations of theq-oscillator algebra and Askey–Wilson polynomials [PDF]
, 2017 A construction is given of the most general representations of the q-oscillator algebra where both generators are tridiagonal. It is shown to be connected to the Askey–Wilson polynomials.
Satoshi Tsujimoto +5 more
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Multiple Askey–Wilson polynomials and related basic hypergeometric multiple orthogonal polynomials [PDF]
, 2020 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.
Jean Paul Nuwacu +3 more
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Expansions in Askey–Wilson polynomials via Bailey transform
Journal of Mathematical Analysis and Applications, 2017 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zeya Jia, Jiang Zeng
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The Askey–Wilson polynomials and q-Sturm–Liouville problems [PDF]
Mathematical Proceedings of the Cambridge Philosophical Society, 1994 We find the adjoint of the Askey–Wilson divided difference operator with respect to the inner product on L2(–1, 1, (1– x2)½dx) defined as a Cauchy principal value and show that the Askey-Wilson polynomials are solutions of a q-Sturm–Liouville problem ...
B. M. Brown, W. D. Evans, M. Ismail
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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 ...
Ayumu Hoshino +2 more
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Zeros and orthogonality of the Askey-Wilson polynomials for $q$ a root of unity [PDF]
Duke Mathematical Journal, 1996 We study some properties of the Askey-Wilson polynomials (AWP) when q is a primitive Nth root of unity. For general four-parameter AWP, zeros of the Nth polynomial and the orthogonality measure are found explicitly.
V. Spiridonov, A. Zhedanov
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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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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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