Results 21 to 30 of about 3,326,560 (250)
A projection formula for the Askey-Wilson polynomials and an application [PDF]
Proceedings of the American Mathematical Society, 1988 A projection formula for p n ( x ; a , b , c , d | q ) {p_n}(x;a,b,c,d|q) , the Askey-Wilson polynomials, is obtained by using a generalization of Askey and Wilson’s q q
Mizan Rahman
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Moments of Askey-Wilson polynomials [PDF]
Journal of Combinatorial Theory, Series A, 2013 New formulas for the nth moment 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 staircase tableaux.
Dennis Stanton, Jang Soo, Kim
core +11 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
Zhi-Guo Liu
semanticscholar +3 more sources
Bootstrapping and Askey-Wilson polynomials [PDF]
Journal of Mathematical Analysis and Applications, 2014 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.
J. Kim, D. Stanton
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Casoratian identities for the Wilson and Askey-Wilson polynomials [PDF]
Journal of Approximation Theory, 2013 31 pages, 2 figures. Comments and references added.
S. Odake, R. Sasaki
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The non-symmetric Wilson polynomials are the Bannai-Ito polynomials [PDF]
Proceedings of the American Mathematical Society, 2015 The one-variable non-symmetric Wilson polynomials are shown to coincide with the Bannai-Ito polynomials. The isomorphism between the corresponding degenerate double affine Hecke algebra of type $(C_1^{\vee}, C_1)$ and the Bannai-Ito algebra is ...
Vincent X. Genest, L. Vinet, A. Zhedanov
semanticscholar +5 more sources
On the Askey-Wilson and Rogers Polynomials [PDF]
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, [
Mourad E. H. Ismail, Dennis Stanton
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Raising and Lowering Operators for Askey-Wilson Polynomials [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2007 This is a contribution to the Vadim Kuznetsov Memorial Issue on Integrable Systems and Related Topics, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/
Siddhartha Sahi
+9 more sources
Turán Inequalities for Symmetric Askey-Wilson Polynomials [PDF]
Rocky Mountain Journal of Mathematics, 2000 The authors study a renormalized \(A-W\) polynomial \(V_n(x)\). Using the Szász technique they establish the inequalities \[ 0\leq V_n^2(x)-V_{n+1} (x)V_{n-1} (x)\leq K, \] where \(K\) is independent of \(x\). The two inequalities hold under certain conditions upon parameters and variable.
Luís Daniel Abreu, J. Bustoz
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Wilson polynomials/functions and intertwining operators for the generic quantum superintegrable system on the 2-sphere [PDF]
, 2014 The Wilson and Racah polynomials can be characterized as basis functions for irreducible representations of the quadratic symmetry algebra of the quantum superintegrable system on the 2-sphere, HΨ = EΨ, with generic 3-parameter potential.
W. Miller, Qiushi Li
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