Results 1 to 10 of about 3,786,814 (174)
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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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.
europepmc +3 more sources
On the Limit from q-Racah Polynomials to Big q-Jacobi Polynomials [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 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.
Tom H. Koornwinder
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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
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Two-Variable Wilson Polynomials and the Generic Superintegrable System on the 3-Sphere [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2011 We show that the symmetry operators for the quantum superintegrable system on the 3-sphere with generic 4-parameter potential form a closed quadratic algebra with 6 linearly independent generators that closes at order 6 (as differential operators ...
Ernie G. Kalnins +2 more
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Bispectrality of the Complementary Bannai-Ito Polynomials [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2013 A one-parameter family of operators that have the complementary Bannai-Ito (CBI) polynomials as eigenfunctions is obtained. The CBI polynomials are the kernel partners of the Bannai-Ito polynomials and also correspond to a q→−1 limit of the Askey-Wilson ...
Vincent X. Genest +2 more
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Nonsymmetric Askey–Wilson polynomials as vector-valued polynomials [PDF]
Applicable Analysis, 2011 Nonsymmetric Askey-Wilson polynomials are usually written as Laurent polynomials. We write them equivalently as 2-vector-valued symmetric Laurent polynomials.
Tom H Koornwinder, Fethi Bouzeffour
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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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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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