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On the Generalized Askey–Wilson Polynomials [PDF]

Journal of Approximation Theory, 2013
In this paper a generalization of Askey-Wilson polynomials is introduced. These polynomials are obtained from the Askey-Wilson polynomials via the addition of two mass points to the weight function of them at the points ±1. Several properties of such new family are considered, in particular the three-term recurrence relation and the representation as ...
Renato Álvarez-Nodarse
exaly   +8 more sources

Casoratian Identities for the Wilson and Askey–Wilson Polynomials [PDF]

Journal of Approximation Theory, 2015
31 pages, 2 figures. Comments and references added.
Satoru Odake, Ryu Sasaki
exaly   +4 more sources

The Factorization Method for the Askey–Wilson Polynomials

Journal of Computational and Applied Mathematics, 1999
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.
Bangerezako, G, Gaspard Bangerezako
exaly   +5 more sources

Nonsymmetric Askey–Wilson Polynomials as Vector-Valued Polynomials [PDF]

Applicable Analysis, 2011
16 pages. Dedicated to Paul Butzer on the occasion of his 80th birthday. v4: minor correction in (4.14)
Tom H. Koornwinder, Fethi Bouzeffour
exaly   +7 more sources

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.
Jiang Zeng
exaly   +5 more sources

Bootstrapping and Askey–Wilson Polynomials

Journal of Mathematical Analysis and Applications, 2015
The mixed moments for the Askey-Wilson polynomials are found using a bootstrapping method and connection coefficients. A similar bootstrapping idea on generating functions gives a new Askey-Wilson generating function. An important special case of this hierarchy is a polynomial which satisfies a four term recurrence, and its combinatorics is studied.
Jang Soo Kim, Dennis Stanton
exaly   +4 more sources

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On the Askey-Wilson Polynomials

Constructive Approximation, 1992
Classical orthogonal polynomials of a discrete variable on non-uniform lattices were introduced by \textit{R. Askey} and \textit{J. A. Wilson} [SIAM J. Math. Anal. 10, 1008-1016 (1979; Zbl 0437.33014)], and \textit{J. A. Wilson} [ibid. 11, 690-701 (1980; Zbl 0454.33007)] and their main properties were established on the basis of the theory of ...
Sergei K. Suslov, N M Atakishiyev
exaly   +3 more sources

On the Askey–Wilson polynomials and a 𝑞-beta integral

Proceedings of the American Mathematical Society, 2021
A proof of the orthogonality relation for the Askey–Wilson polynomials is given by using a generating function for the Askey–Wilson polynomials and the uniqueness of a rational function expansion. We further use the orthogonality relation for the Askey–Wilson polynomials and a
openaire   +1 more source

“Hidden symmetry” of Askey-Wilson polynomials

Theoretical and Mathematical Physics, 1991
See the review in Zbl 0744.33009.
openaire   +1 more source

Some Functions that Generalize the Askey-Wilson Polynomials

Communications in Mathematical Physics, 1997
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Grunbaum, FA, Haine, Luc
openaire   +2 more sources