Results 1 to 10 of about 7,854 (155)
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
core +6 more sources
Generalized Burchnall-Type Identities for Orthogonal Polynomials and Expansions [PDF]
Applicable Analysis, 2018 Burchnall's method to invert the Feldheim-Watson linearization formula for the Hermite polynomials is extended to all polynomial families in the Askey-scheme and its $q$-analogue.
Ismail, Mourad E. H. +2 more
core +13 more sources
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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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
doaj +11 more sources
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
semanticscholar +5 more sources
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
Proof of two conjectures on Askey-Wilson polynomials [PDF]
Proceedings of the American Mathematical Society, 2023 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
openalex +3 more sources
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
semanticscholar +5 more sources
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
doaj +5 more sources
The Universal Askey-Wilson Algebra [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2011 In 1992 A. Zhedanov introduced the Askey-Wilson algebra AW=AW(3) and used it to describe the Askey-Wilson polynomials. In this paper we introduce a central extension Δ of AW, obtained from AW by reinterpreting certain parameters as central elements in ...
Paul Terwilliger
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