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Equilibrium Positions, Shape Invariance and Askey-Wilson Polynomials [PDF]
Journal of Mathematical Physics, 2004 We show that the equilibrium positions of the Ruijsenaars-Schneider-van Diejen systems with the trigonometric potential are given by the zeros of the Askey-Wilson polynomials with five parameters.
Askey R. +3 more
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The structure relation for Askey–Wilson polynomials [PDF]
Journal of Computational and Applied Mathematics, 2006 An explicit structure relation for Askey-Wilson polynomials is given. This involves a divided q-difference operator which is skew symmetric with respect to the Askey-Wilson inner product and which sends polynomials of degree n to polynomials of degree n+1.
Tom H. Koornwinder
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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},
Dharma P. Gupta, David R. Masson
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Terminating Basic Hypergeometric Representations and Transformations for the Askey-Wilson Polynomials. [PDF]
Symmetry (Basel), 2020 Cohl HS, Costas-Santos RS, Ge L.
europepmc +3 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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Generalized Bochner theorem: characterization of the Askey-Wilson polynomials [PDF]
Journal of Computational and Applied Mathematics, 2007 Assume that there is a set of monic polynomials $P_n(z)$ satisfying the second-order difference equation $$ A(s) P_n(z(s+1)) + B(s) P_n(z(s)) + C(s) P_n(z(s-1)) = _n P_n(z(s)), n=0,1,2,..., N$$ where $z(s), A(s), B(s), C(s)$ are some functions of the discrete argument $s$ and $N$ may be either finite or infinite. The irreducibility condition $A(s-1)C(
Luc Vinet, Alexei Zhedanov
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An eigenvalue problem for the associated Askey-Wilson polynomials [PDF]
, 2012 AmS-LaTeX; 15 ...
Andrea Bruder +2 more
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Discrete Analogues of the Erdélyi Type Integrals for Hypergeometric Functions
Journal of Mathematics, Volume 2022, Issue 1, 2022., 2022 Gasper followed the fractional calculus proof of an Erdélyi integral to derive its discrete analogue in the form of a hypergeometric expansion. To give an alternative proof, we derive it by following a procedure analogous to a triple series manipulation‐based proof of the Erdélyi integral, due to “Joshi and Vyas”. Motivated from this alternative way of
Yashoverdhan Vyas +5 more
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A Linear Map Acts as a Leonard Pair with Each of the Generators of U(sl2)
International Journal of Mathematics and Mathematical Sciences, Volume 2020, Issue 1, 2020., 2020 Let ℱ denote an algebraically closed field with a characteristic not two. Fix an integer d ≥ 3; let x, y, and z be the equitable basis of sl2 over ℱ. Let V denote an irreducible sl2‐module with dimension d + 1; let A ∈ End(V). In this paper, we show that if each of the pairs A, x, A, y, and A, z acts on V as a Leonard pair, then these pairs are of ...
Hasan Alnajjar, Luca Vitagliano
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Mathematical Problems in Engineering, Volume 2020, Issue 1, 2020., 2020 The optimization of oil field development scheme considering the uncertainty of reservoir model is a challenging and difficult problem in reservoir engineering design. The most common method used in this regard is to generate multiple models based on statistical analysis of uncertain reservoir parameters and requires a large number of simulations to ...
Liang Zhang +7 more
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