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The Associated Askey-Wilson Polynomials [PDF]
Transactions of the American Mathematical Society, 1991 The most general system of basic hypergeometric orthogonal polynomials are the Askey-Wilson polynomials, which are given as a basic hypergeometric series \(_ 4\Phi_ 3\). Like all orthogonal polynomials they satisfy a three-term recurrence relation \[ 2xp_ n(x)=A_ np_{n+1}(x)+B_ np_ n(x)+C_ np_{n-1}(x). \] The recurrence coefficients \(A_ n\), \(B_ n\),
Ismail, Mourad E. H., Rahman, Mizan
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Befriending Askey–Wilson polynomials [PDF]
Infinite Dimensional Analysis, Quantum Probability and Related Topics, 2014 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. In doing so we express AW density as a product of the density that makes q-Hermite polynomials orthogonal times a ...
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Askey-Wilson Polynomials and Branching Laws
, 2022 Connection coefficient formulas for special functions describe change of basis matrices under a parameter change, for bases formed by the special functions. Such formulas are related to branching questions in representation theory. The Askey-Wilson polynomials are one of the most general 1-variable special functions.
Back, Allen +3 more
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Multi-indexed Wilson and Askey–Wilson polynomials [PDF]
Journal of Physics A: Mathematical and Theoretical, 2013 As the third stage of the project multi-indexed orthogonal polynomials, we present, in the framework of 'discrete quantum mechanics' with pure imaginary shifts in one dimension, the multi-indexed Wilson and Askey-Wilson polynomials. They are obtained from the original Wilson and Askey-Wilson polynomials by multiple application of the discrete analogue ...
Odake, Satoru, Sasaki, Ryu
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Journal of Advanced Research, 2010 Formulae expressing explicitly the q-difference derivatives and the moments of the polynomials Pn(x ; q) ∈ T (T ={Pn(x ; q) ∈ Askey–Wilson polynomials: Al-Salam-Carlitz I, Discrete q-Hermite I, Little (Big) q-Laguerre, Little (Big) q-Jacobi, q-Hahn ...
Eid H. Doha, Hany M. Ahmed
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A characterization of Askey-Wilson polynomials
Proceedings of the American Mathematical Society, 2019 We show that the only monic orthogonal polynomials $\{P_n\}_{n=0}^{\infty}$ that satisfy $$ (x)\mathcal{D}_{q}^2P_{n}(x)=\sum_{j=-2}^{2}a_{n,n+j}P_{n+j}(x),\; x=\cos ,\;~ a_{n,n-2}\neq 0,~ n=2,3,\dots,$$ where $ (x)$ is a polynomial of degree at most $4$ and $\mathcal{D}_{q}$ is the Askey-Wilson operator, are Askey-Wilson polynomials and their ...
Nangho, Maurice Kenfack +1 more
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Exceptional 𝑞-Askey-Wilson polynomials and continued fractions [PDF]
Proceedings of the American Mathematical Society, 1991 Two linearly independent solutions of the three-term recurrence relation for the q q -Askey-Wilson polynomials are obtained for the special cases a b c d = q m , m = 1 , 2 , … abcd = {q^m},
Gupta, Dharma P., Masson, David R.
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Diagonalization of the Heun-Askey-Wilson operator, Leonard pairs and the algebraic Bethe ansatz
Nuclear Physics B, 2019 An operator of Heun-Askey-Wilson type is diagonalized within the framework of the algebraic Bethe ansatz using the theory of Leonard pairs. For different specializations and the generic case, the corresponding eigenstates are constructed in the form of ...
Pascal Baseilhac, Rodrigo A. Pimenta
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Application of Galerkin Method to Kirchhoff Plates Stochastic Bending Problem
International Scholarly Research Notices, Volume 2014, Issue 1, 2014., 2014 In this paper, the Galerkin method is used to obtain approximate solutions for Kirchhoff plates stochastic bending problem with uncertainty over plates flexural rigidity coefficient. The uncertainty in the rigidity coefficient is represented by means of parameterized stochastic processes. A theorem of Lax‐Milgram type, about existence and uniqueness of
Cláudio Roberto Ávila da Silva Júnior +5 more
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Advances in Mathematical Physics, Volume 2009, Issue 1, 2009., 2009 In this paper, we apply to (almost) all the “named” polynomials of the Askey scheme, as defined by their standard three‐term recursion relations, the machinery developed in previous papers. For each of these polynomials we identify at least one additional recursion relation involving a shift in some of the parameters they feature, and for several of ...
M. Bruschi +3 more
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