Results 11 to 20 of about 45,476 (265)
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.
Włodek Bryc, Jacek Wesołowski
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Nonsymmetric Askey–Wilson polynomials as vector-valued polynomials [PDF]
Applicable Analysis, 2010 16 pages. Dedicated to Paul Butzer on the occasion of his 80th birthday. v4: minor correction in (4.14)
Tom H. Koornwinder +3 more
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On the Limit from q-Racah Polynomials to Big q-Jacobi Polynomials [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2011 A limit formula from q-Racah polynomials to big q-Jacobi polynomials is given which can be considered as a limit formula for orthogonal polynomials.
Tom H. Koornwinder
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Two-Variable Wilson Polynomials and the Generic Superintegrable System on the 3-Sphere [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2011 We show that the symmetry operators for the quantum superintegrable system on the 3-sphere with generic 4-parameter potential form a closed quadratic algebra with 6 linearly independent generators that closes at order 6 (as differential operators ...
Ernie G. Kalnins +2 more
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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
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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 \(A_ n\), \(B_ n\),
Mourad E. H. Ismail, Mizan Rahman
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Scholarpedia, 2012 Askey-Wilson polynomial refers to a four-parameter family of q-hypergeometric orthogonal polynomials which contains all families of classical orthogonal polynomials (in the wide sense) as special or limit cases.
Tom H. Koornwinder
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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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Non-symmetric Jacobi and Wilson type polynomials [PDF]
International Mathematics Research Notices, 2005 Consider a root system of type $BC_1$ on the real line $\mathbb R$ with general positive multiplicities. The Cherednik-Opdam transform defines a unitary operator from an $L^2$-space on $\mathbb R$ to a $L^2$-space of $\mathbb C^2$-valued functions on $\mathbb R^+$ with the Harish-Chandra measure $|c(\lam)|^{-2}d\lam$.
Lizhong Peng, Genkai Zhang
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Wilson polynomials and the Lorentz transformation properties of the parity operator [PDF]
, 2005 The parity operator for a parity-symmetric quantum field theory transforms as an infinite sum of irreducible representations of the homogeneous Lorentz group.
Carl M. Bender +2 more
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