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Moments of Askey-Wilson polynomials [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 New formulas for the $n^{\mathrm{th}}$ moment $\mu_n(a,b,c,d;q)$ of the Askey-Wilson polynomials are given. These are derived using analytic techniques, and by considering three combinatorial models for the moments: Motzkin paths, matchings, and ...
Jang Soo Kim, Dennis Stanton
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Raising and Lowering Operators for Askey-Wilson Polynomials [PDF]
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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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.
Koornwinder, T.H.; id_orcid
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Askey-Wilson Polynomials and Branching Laws [PDF]
Journal of Lie Theory, 2023 Connection coefficient formulas for special functions describe change of basis matrices under a parameter change, for bases formed by the special functions. Such formulas are related to branching questions in representation theory. The Askey-Wilson polynomials are one of the most general 1-variable special functions.
Back, Allen +3 more
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On the Askey-Wilson and Rogers Polynomials
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, [
Ismail, Mourad E. H., Stanton, Dennis
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The structure relation for Askey–Wilson polynomials
Journal of Computational and Applied Mathematics, 2007 An explicit structure relation for Askey-Wilson polynomials is given. This involves a divided q-difference operator which is skew symmetric with respect to the Askey-Wilson inner product and which sends polynomials of degree n to polynomials of degree n+1.
Koornwinder, T.H.; id_orcid
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Multi-indexed Wilson and Askey–Wilson polynomials [PDF]
Journal of Physics A: Mathematical and Theoretical, 2013 As the third stage of the project multi-indexed orthogonal polynomials, we present, in the framework of 'discrete quantum mechanics' with pure imaginary shifts in one dimension, the multi-indexed Wilson and Askey-Wilson polynomials. They are obtained from the original Wilson and Askey-Wilson polynomials by multiple application of the discrete analogue ...
Odake, Satoru, Sasaki, Ryu
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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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Contractions of 2D 2nd Order Quantum Superintegrable Systems and the Askey Scheme for Hypergeometric Orthogonal Polynomials [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2013 We show explicitly that all 2nd order superintegrable systems in 2 dimensions are limiting cases of a single system: the generic 3-parameter potential on the 2-sphere, S9 in our listing.
Ernest G. Kalnins +2 more
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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
Mizan Rahman
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