A characterization of the Rogers q-hermite polynomials
International Journal of Mathematics and Mathematical Sciences, 1995 In this paper we characterize the Rogers q-Hermite polynomials as the only orthogonal polynomial set which is also 𝒟q-Appell where 𝒟q is the Askey-Wilson finite difference operator.
Waleed A. Al-Salam
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Askey-Wilson polynomials and the quantum SU(2) group: survey and applications [PDF]
Acta Applicandae Mathematicae - An International Survey Journal on Applying Mathematics and Mathematical Applications, 1994 Generalised matrix elements of the irreducible representations of the quantum SU(2) group are defined using certain orthonormal bases of the representation space.
Erik Koelink
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Askey–Wilson polynomials, quadratic harnesses and martingales [PDF]
, 2010 We use orthogonality measures of Askey--Wilson polynomials to construct Markov processes with linear regressions and quadratic conditional variances. Askey--Wilson polynomials are orthogonal martingale polynomials for these processes.
Włodek Bryc, Jacek Wesołowski
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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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Raising and Lowering Operators for Askey-Wilson Polynomials
Symmetry, Integrability and Geometry: Methods and Applications, 2007 In this paper we describe two pairs of raising/lowering operators for Askey-Wilson polynomials, which result from constructions involving very different techniques. The first technique is quite elementary, and depends only on the ''classical'' properties
Siddhartha Sahi
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Zeros and orthogonality of the Askey-Wilson polynomials for q a root of unity [PDF]
, 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. P. Spiridonov, Alexei Zhedanov
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Degenerations of Sklyanin algebra and Askey-Wilson polynomials [PDF]
, 1993 A new trigonometric degeneration of the Sklyanin algebra is found and the functional realization of its representations in space of polynomials in one variable is studied. A further contraction gives the standard quantum algebra Uq(sl(2)).
A S Gorsky, A V Zabrodin
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Degenerate Sklyanin algebras, Askey–Wilson polynomials and Heun operators [PDF]
Journal of Physics A: Mathematical and Theoretical, 2020 The q-difference equation, the shift and the contiguity relations of the Askey–Wilson polynomials are cast in the framework of the three and four-dimensional degenerate Sklyanin algebras ska3 and ska4 .
J. Gaboriaud +3 more
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Discrete Analogues of the Erdélyi Type Integrals for Hypergeometric Functions
Journal of Mathematics, Volume 2022, Issue 1, 2022., 2022 Gasper followed the fractional calculus proof of an Erdélyi integral to derive its discrete analogue in the form of a hypergeometric expansion. To give an alternative proof, we derive it by following a procedure analogous to a triple series manipulation‐based proof of the Erdélyi integral, due to “Joshi and Vyas”. Motivated from this alternative way of
Yashoverdhan Vyas +5 more
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Discrete Darboux transformations, the discrete-time Toda lattice, and the Askey–Wilson polynomials [PDF]
, 1995 V. P. Spiridonov, Alexei Zhedanov
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