Results 81 to 90 of about 2,395 (106)

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.
Kim, Jang Soo, Stanton, Dennis
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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.
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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 ...
Atakishiev, N. M., Suslov, S. K.
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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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?Hidden symmetry? of Askey-Wilson polynomials

Theoretical and Mathematical Physics, 1991
See the review in Zbl 0744.33009.
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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
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Some Functions that Generalize the Askey-Wilson Polynomials

Communications in Mathematical Physics, 1997
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Grünbaum, F. Alberto, Haine, Luc
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On the Zeros of the Askey–Wilson Polynomials, with Applications to Coding Theory

SIAM Journal on Mathematical Analysis, 1987
In a symmetric association scheme that is (P and Q)-polynomial, the P and Q eigenmatrices are given by balanced \({}_ 4\Phi_ 3\) Askey-Wilson polynomials. In this paper, the parameters of the Askey-Wilson polynomial are classified so that its zeros are not contained in its spectrum. These results, together with theorems of Biggs and Delsarte, imply the
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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.
Jia, Zeya, Zeng, Jiang
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Askey-Wilson polynomials, kernel polynomials and association schemes

Graphs and Combinatorics, 1993
For many of the classical association schemes, there are specific sets of orthogonal polynomials associated with them. When these can be found explicitly, the polynomials can be given as hypergeometric or basic hypergeometric series. A new association scheme was constructed by \textit{A. A. Ivanov}, \textit{M. E. Muzichuk} and \textit{V. A. Ustimenko} [
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