Askey–Wilson polynomials
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1: 18.29 Asymptotic Approximations for -Hahn and Askey–Wilson Classes
§18.29 Asymptotic Approximations for -Hahn and Askey–Wilson Classes
►Ismail (1986) gives asymptotic expansions as , with and other parameters fixed, for continuous -ultraspherical, big and little -Jacobi, and Askey–Wilson polynomials. …For Askey–Wilson the leading term is given by …2: 18.28 Askey–Wilson Class
§18.28 Askey–Wilson Class
… ►Both the Askey–Wilson polynomials and the -Racah polynomials can best be described as functions of (resp. … ►§18.28(ii) Askey–Wilson Polynomials
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18.28.1
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►For and see Koekoek et al. (2010, Eq. (14.2.2)).
3: 18.1 Notation
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Askey–Wilson: .
4: Tom H. Koornwinder
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►Koornwinder has published numerous papers on special functions, harmonic analysis, Lie groups, quantum groups, computer algebra, and their interrelations, including an interpretation of Askey–Wilson polynomials on quantum SU(2), and a five-parameter extension (the Macdonald–Koornwinder polynomials) of Macdonald’s polynomials for root systems BC.
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5: Richard A. Askey
6: 18.21 Hahn Class: Interrelations
7: 18.30 Associated OP’s
8: Bibliography K
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Askey-Wilson Polynomials for Root Systems of Type
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In Hypergeometric Functions on Domains of Positivity, Jack
Polynomials, and Applications (Tampa, FL, 1991),
Contemp. Math., Vol. 138, pp. 189–204.
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Askey-Wilson polynomial.
Scholarpedia 7 (7), pp. 7761.
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9: 18.37 Classical OP’s in Two or More Variables
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►In one variable they are essentially ultraspherical, Jacobi, continuous -ultraspherical, or Askey–Wilson polynomials.
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10: Bibliography C
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On the zeros of the Askey-Wilson polynomials, with applications to coding theory.
SIAM J. Math. Anal. 18 (1), pp. 191–207.
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