About the Project
NIST

Askey–Wilson polynomials

AdvancedHelp

(0.002 seconds)

1—10 of 19 matching pages

1: 18.29 Asymptotic Approximations for q -Hahn and Askey–Wilson Classes
§18.29 Asymptotic Approximations for q -Hahn and AskeyWilson Classes
Ismail (1986) gives asymptotic expansions as n , with x and other parameters fixed, for continuous q -ultraspherical, big and little q -Jacobi, and AskeyWilson polynomials. …For AskeyWilson p n ( cos θ ; a , b , c , d | q ) the leading term is given by …
2: 18.28 Askey–Wilson Class
§18.28 AskeyWilson Class
Both the AskeyWilson polynomials and the q -Racah polynomials can best be described as functions of z (resp. …
§18.28(ii) AskeyWilson Polynomials
18.28.1 p n ( cos θ ) = p n ( cos θ ; a , b , c , d | q ) = a - n = 0 n q ( a b q , a c q , a d q ; q ) n - ( q - n , a b c d q n - 1 ; q ) ( q ; q ) j = 0 - 1 ( 1 - 2 a q j cos θ + a 2 q 2 j ) = a - n ( a b , a c , a d ; q ) n ϕ 3 4 ( q - n , a b c d q n - 1 , a e i θ , a e - i θ a b , a c , a d ; q , q ) .
For ω y and h n see Koekoek et al. (2010, Eq. (14.2.2)).
3: 18.1 Notation
  • AskeyWilson: p n ( x ; a , b , c , d | q ) .

  • 4: Tom H. Koornwinder
    Koornwinder has published numerous papers on special functions, harmonic analysis, Lie groups, quantum groups, computer algebra, and their interrelations, including an interpretation of AskeyWilson polynomials on quantum SU(2), and a five-parameter extension (the Macdonald–Koornwinder polynomials) of Macdonald’s polynomials for root systems BC. …
    5: Richard A. Askey
     Wilson), introduced the Askey-Wilson polynomials. …
    6: 18.21 Hahn Class: Interrelations
    See accompanying text
    Figure 18.21.1: Askey scheme. … Magnify
    7: 18.30 Associated OP’s
    For associated AskeyWilson polynomials see Rahman (2001).
    8: Bibliography K
  • T. H. Koornwinder (1992) Askey-Wilson Polynomials for Root Systems of Type B C . In Hypergeometric Functions on Domains of Positivity, Jack Polynomials, and Applications (Tampa, FL, 1991), Contemp. Math., Vol. 138, pp. 189–204.
  • T. H. Koornwinder (2012) Askey-Wilson polynomial. Scholarpedia 7 (7), pp. 7761.
  • 9: 18.37 Classical OP’s in Two or More Variables
    In one variable they are essentially ultraspherical, Jacobi, continuous q -ultraspherical, or AskeyWilson polynomials. …
    10: Bibliography C
  • L. Chihara (1987) On the zeros of the Askey-Wilson polynomials, with applications to coding theory. SIAM J. Math. Anal. 18 (1), pp. 191–207.