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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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Wilson Polynomials and the Lorentz Transformation Properties of the Parity Operator [PDF]
, 2004 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 +4 more
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The factorization method for the Askey-Wilson polynomials.
Journal of Computational and Applied Mathematics, 1998 A special Infeld-Hall factorization is given for the Askey-Wilson second order q-difference operator. It is then shown how to deducd a generalization of the corresponding Askey-Wilson polynomials.
Gaspard Bangerezako
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Multiple Wilson and Jacobi–Piñeiro polynomials
Journal of Approximation Theory, 2005 22 pages, 2 ...
Bernhard Beckermann +2 more
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Tridiagonal representations of the q-oscillator algebra and Askey–Wilson polynomials [PDF]
, 2016 A construction is given of the most general representations of the q-oscillator algebra where both generators are tridiagonal. It is shown to be connected to the Askey–Wilson polynomials.
S. Tsujimoto, L. Vinet, A. Zhedanov
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Expansions in the Askey{Wilson Polynomials
Journal of Mathematical Analysis and Applications, 2015 Abstract We give a general expansion formula of functions in the Askey–Wilson polynomials and using Askey–Wilson orthogonality we evaluate several integrals. Moreover we give a general expansion formula of functions in polynomials of Askey–Wilson type, which are not necessarily orthogonal.
M. Ismail, D. Stanton
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On Some Limit Cases of Askey–Wilson Polynomials
Journal of Approximation Theory, 1998 The authors derive the classical orthogonality relations and norm evaluations for the \(q\)-Racah and \(q\)-Jacobi polynomials by taking limits in the orthogonality relations and norm evaluations for the Askey-Wilson polynomials [\textit{R. Askey} and \textit{J. Wilson}, Mem. Am. Math. Soc. 54, No. 319, 1-55 (1985; Zbl 0572.33012)].
Jasper V. Stokman, 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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A quadratic formula for basic hypergeometric series related to Askey-Wilson polynomials [PDF]
, 2012 We prove a general quadratic formula for basic hypergeometric series, from which simple proofs of several recent determinant and Pfaffian formulas are obtained. A special case of the quadratic formula is actually related to a Gram determinant formula for
Victor J. W. Guo +3 more
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