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Wilson polynomials

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11: Bibliography I
  • M. E. H. Ismail, J. Letessier, G. Valent, and J. Wimp (1990) Two families of associated Wilson polynomials. Canad. J. Math. 42 (4), pp. 659–695.
  • M. E. H. Ismail (1986) Asymptotics of the Askey-Wilson and q -Jacobi polynomials. SIAM J. Math. Anal. 17 (6), pp. 1475–1482.
  • 12: Bibliography Z
  • A. S. Zhedanov (1991) “Hidden symmetry” of Askey-Wilson polynomials. Theoret. and Math. Phys. 89 (2), pp. 1146–1157.
  • 13: Bibliography N
  • M. Noumi and J. V. Stokman (2004) Askey-Wilson polynomials: an affine Hecke algebra approach. In Laredo Lectures on Orthogonal Polynomials and Special Functions, Adv. Theory Spec. Funct. Orthogonal Polynomials, pp. 111–144.
  • 14: 18.37 Classical OP’s in Two or More Variables
    In one variable they are essentially ultraspherical, Jacobi, continuous q -ultraspherical, or Askey–Wilson polynomials. …
    15: Errata
  • Equation (18.28.1)
    18.28.1 p n ( x ) = p n ( x ; 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 x + a 2 q 2 j ) ,
    18.28.1_5 R n ( z ) = R n ( z ; a , b , c , d | q ) = p n ( 1 2 ( z + z 1 ) ; a , b , c , d | q ) a n ( a b , a c , a d ; q ) n = ϕ 3 4 ( q n , a b c d q n 1 , a z , a z 1 a b , a c , a d ; q , q )

    Previously we presented all the information of these formulas in one equation

    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 ) .
  • 16: Bibliography G
  • V. X. Genest, L. Vinet, and A. Zhedanov (2016) The non-symmetric Wilson polynomials are the Bannai-Ito polynomials. Proc. Amer. Math. Soc. 144 (12), pp. 5217–5226.
  • 17: Bibliography M
  • D. R. Masson (1991) Associated Wilson polynomials. Constr. Approx. 7 (4), pp. 521–534.
  • 18: 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.
  • 19: 18.30 Associated OP’s
    For associated Askey–Wilson polynomials see Rahman (2001). …
    20: Bibliography W
  • J. A. Wilson (1978) Hypergeometric Series, Recurrence Relations and Some New Orthogonal Polynomials. Ph.D. Thesis, University of Wisconsin, Madison, WI.
  • J. A. Wilson (1980) Some hypergeometric orthogonal polynomials. SIAM J. Math. Anal. 11 (4), pp. 690–701.
  • J. A. Wilson (1991) Asymptotics for the F 3 4 polynomials. J. Approx. Theory 66 (1), pp. 58–71.