Results 41 to 50 of about 2,394 (105)
Equivalences of the Multi-Indexed Orthogonal Polynomials [PDF]
, 2013 Multi-indexed orthogonal polynomials describe eigenfunctions of exactly solvable shape-invariant quantum mechanical systems in one dimension obtained by the method of virtual states deletion.
Odake, Satoru
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The Universal Askey-Wilson Algebra and DAHA of Type (C_1^∨,C_1)
Symmetry, Integrability and Geometry: Methods and Applications, 2013 Around 1992 A. Zhedanov introduced the Askey-Wilson algebra AW(3). Recently we introduced a central extension $Delta_q$ of AW(3) called the universal Askey-Wilson algebra.
Paul Terwilliger
doaj +1 more source
Turán Inequalities for Symmetric Askey-Wilson Polynomials
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.
Abreu, L.D., Bustoz, J.
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Recurrence Relations of the Multi-Indexed Orthogonal Polynomials IV : closure relations and creation/annihilation operators [PDF]
, 2016 We consider the exactly solvable quantum mechanical systems whose eigenfunctions are described by the multi-indexed orthogonal polynomials of Laguerre, Jacobi, Wilson and Askey-Wilson types.
Odake, Satoru
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Properties of some families of hypergeometric orthogonal polynomials in several variables
, 1996 Limiting cases are studied of the Koornwinder-Macdonald multivariable generalization of the Askey-Wilson polynomials. We recover recently and not so recently introduced families of hypergeometric orthogonal polynomials in several variables consisting of ...
van Diejen, Jan F.
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Continuous −1$-1$ hypergeometric orthogonal polynomials
Studies in Applied Mathematics, Volume 153, Issue 3, October 2024.Abstract The study of −1$-1$ orthogonal polynomials viewed as q→−1$q\rightarrow -1$ limits of the q$q$‐orthogonal polynomials is pursued. This paper presents the continuous polynomials part of the −1$-1$ analog of the q$q$‐Askey scheme. A compendium of the properties of all the continuous −1$-1$ hypergeometric polynomials and their connections is ...
Jonathan Pelletier +2 more
wiley +1 more source
Double Affine Hecke Algebras of Rank 1 and the Z_3-Symmetric Askey-Wilson Relations
Symmetry, Integrability and Geometry: Methods and Applications, 2010 We consider the double affine Hecke algebra H=H(k_0,k_1,k_0^v,k_1^v;q) associated with the root system (C_1^v,C_1). We display three elements x, y, z in H that satisfy essentially the Z_3-symmetric Askey-Wilson relations.
Paul Terwilliger, Tatsuro Ito
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Symmetry, Integrability and Geometry: Methods and Applications, 2013 We show explicitly that all 2nd order superintegrable systems in 2 dimensions are limiting cases of a single system: the generic 3-parameter potential on the 2-sphere, S9 in our listing.
Ernest G. Kalnins +2 more
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The Askey–Wilson polynomials and q-Sturm–Liouville problems [PDF]
Mathematical Proceedings of the Cambridge Philosophical Society, 1996 AbstractWe find the adjoint of the Askey–Wilson divided difference operator with respect to the inner product on L2(–1, 1, (1– x2)½dx) defined as a Cauchy principal value and show that the Askey-Wilson polynomials are solutions of a q-Sturm–Liouville problem.
Brown, B. Malcolm +2 more
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The structure relation for Askey–Wilson polynomials
Journal of Computational and Applied Mathematics, 2007 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.
openaire +5 more sources