Results 11 to 20 of about 3,326,560 (250)
On the Krall-type Askey-Wilson Polynomials [PDF]
Journal of Approximation Theory, 2012 In this paper the general Krall-type Askey-Wilson polynomials are 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 $\pm1$.
Askey +24 more
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Proof of two conjectures on Askey-Wilson polynomials [PDF]
Proceedings of the American Mathematical Society, 2022 We give positive answer to two conjectures posed by M. E. H Ismail in his monograph [Classical and quantum orthogonal polynomials in one variable, Cambridge University Press, Cambridge, 2005]. These results generalize the classical problems of Sonine and
K. Castillo, D. Mbouna
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On Another Characterization of Askey-Wilson Polynomials [PDF]
Results in Mathematics, 2022 In this paper we show that the only sequences of orthogonal polynomials (Pn)n≥0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage ...
D. Mbouna, A. Suzuki
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A characterization of Askey-Wilson polynomials [PDF]
Proceedings of the American Mathematical Society, 2017 We show that the only monic orthogonal polynomials $\{P_n\}_{n=0}^{\infty}$ that satisfy $$\pi(x)\mathcal{D}_{q}^2P_{n}(x)=\sum_{j=-2}^{2}a_{n,n+j}P_{n+j}(x),\; x=\cos\theta,\;~ a_{n,n-2}\neq 0,~ n=2,3,\dots,$$ where $\pi(x)$ is a polynomial of degree at
M. K. Nangho, K. Jordaan
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Befriending Askey-Wilson polynomials [PDF]
Infinite Dimensional Analysis, Quantum Probability and Related Topics, 2011 We recall five families of polynomials constituting a part of the so-called Askey–Wilson scheme. We do this to expose properties of the Askey–Wilson (AW) polynomials that constitute the last, most complicated element of this scheme.
P. Szabłowski
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Askey--Wilson polynomials, quadratic harnesses and martingales [PDF]
The Annals of Probability, 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.Comment: Published ...
Bryc, Włodek, Wesołowski, Jacek
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Terminating Basic Hypergeometric Representations and Transformations for the Askey-Wilson Polynomials. [PDF]
Symmetry (Basel), 2020 In this survey paper, we exhaustively explore the terminating basic hypergeometric representations of the Askey–Wilson polynomials and the corresponding terminating basic hypergeometric transformations that these polynomials satisfy.
Cohl HS, Costas-Santos RS, Ge L.
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On the Limit from q-Racah Polynomials to Big q-Jacobi Polynomials [PDF]
Applicable Analysis, 2011 A limit formula from q-Racah polynomials to big q-Jacobi polynomials is given which can be considered as a limit formula for orthogonal polynomials.
Koornwinder, Tom H.
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Remarks on Askey–Wilson polynomials and Meixner polynomials of the second kind [PDF]
The Ramanujan Journal, 2021 The purpose of this note is to characterize all the sequences of orthogonal polynomials (Pn)n≥0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs ...
K. Castillo, D. Mbouna, J. Petronilho
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Jacobi Ensemble, Hurwitz Numbers and Wilson Polynomials [PDF]
Letters in Mathematical Physics, 2020 We express the topological expansion of the Jacobi Unitary Ensemble in terms of triple monotone Hurwitz numbers. This completes the combinatorial interpretation of the topological expansion of the classical unitary invariant matrix ensembles.
Massimo Gisonni, T. Grava, Giulio Ruzza
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