Results 1 to 10 of about 442,685 (123)
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 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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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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Staircase tableaux, the asymmetric exclusion process, and Askey-Wilson polynomials. [PDF]
Proc Natl Acad Sci U S A, 2010 We introduce some combinatorial objects called staircase tableaux, which have cardinality 4nn !, and connect them to both the asymmetric exclusion process (ASEP) and Askey-Wilson polynomials.
Corteel S, Williams LK.
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A characterization of Askey-Wilson polynomials [PDF]
Proceedings of the American Mathematical Society, 2018 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
Maurice Kenfack Nangho, Kerstin Jordaan
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Tridiagonal representations of theq-oscillator algebra and Askey–Wilson polynomials [PDF]
, 2017 A construction is given of the most general representations of the q-oscillator algebra where both generators are tridiagonal. It is shown to be connected to the Askey–Wilson polynomials.
Satoshi Tsujimoto +2 more
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Askey--Wilson polynomials and a double $q$-series transformation formula with twelve parameters [PDF]
Proceedings of the American Mathematical Society, 2018 The Askey--Wilson polynomials are the most general classical orthogonal polynomials that are known and the Nassrallah--Rahman integral is a very general extension of Euler's integral representation of the classical $_2F_1$ function. Based on a $q$-series
Zhiguo Liu
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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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A generalization of Mehta-Wang determinant and Askey-Wilson polynomials [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 Motivated by the Gaussian symplectic ensemble, Mehta and Wang evaluated the $n×n$ determinant $\det ((a+j-i)Γ (b+j+i))$ in 2000. When $a=0$, Ciucu and Krattenthaler computed the associated Pfaffian $\mathrm{Pf}((j-i)Γ (b+j+i))$ with an application to the
Victor J. W. Guo +3 more
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