Askey-Wilson polynomials: an affine Hecke algebraic approach
, 2000 We study Askey-Wilson type polynomials using representation theory of the double affine Hecke algebra. In particular, we prove bi-orthogonality relations for non-symmetric and anti-symmetric Askey-Wilson polynomials with respect to a complex measure.
Noumi, M., Stokman, J.V.
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Two limit transitions involving multivariable BC type Askey-Wilson polynomials [PDF]
, 1997 Jasper V. Stokman
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Addition formulas for q-special functions
, 1995 A general addition formula for a two-parameter family of Askey-Wilson polynomials is derived from the quantum $SU(2)$ group theoretic interpretation. This formula contains most of the previously known addition formulas for $q$-Legendre polynomials as ...
Koelink, Erik
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On three dimensional multivariate version of q-Normal distribution and probabilistic interpretations of Askey–Wilson, Al-Salam–Chihara and q-ultraspherical polynomials [PDF]
, 2019 Paweł J. Szabłowski
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A note on the $O_q(\hat{sl_2})$ algebra
, 2010 An explicit homomorphism that relates the elements of the infinite dimensional non-Abelian algebra generating $O_q(\hat{sl_2})$ currents and the standard generators of the $q-$Onsager algebra is proposed.
Baseilhac, P., Belliard, S.
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Nonsymmetric Askey–Wilson polynomials and Q-polynomial distance-regular graphs
Journal of Combinatorial Theory, Series A, 2017 In his famous theorem (1982), Douglas Leonard characterized the $q$-Racah polynomials and their relatives in the Askey scheme from the duality property of $Q$-polynomial distance-regular graphs. In this paper we consider a nonsymmetric (or Laurent) version of the $q$-Racah polynomials in the above situation.
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On a generalization of the Rogers generating function. [PDF]
J Math Anal Appl, 2019 Cohl HS, Costas-Santos RS, Wakhare TV.
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Some generating functions and projection formula for the associated Askey-Wilson polynomials.
, 1997 Qazi Tariq
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Degenerations of Sklyanin algebra and Askey-Wilson polynomials [PDF]
, 1993 A. S. Gorsky +3 more
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A quadratic formula for basic hypergeometric series related to Askey-Wilson polynomials [PDF]
, 2012 Victor J. W. Guo +3 more
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