Duke Mathematical Journal

Zeros and orthogonality of the Askey-Wilson polynomials for q a root of unity

Vyacheslav Spiridonov and Alexei Zhedanov

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Article information

Source
Duke Math. J., Volume 89, Number 2 (1997), 283-305.

Dates
First available in Project Euclid: 19 February 2004

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1077241019

Digital Object Identifier
doi:10.1215/S0012-7094-97-08914-6

Mathematical Reviews number (MathSciNet)
MR1460624

Zentralblatt MATH identifier
0882.33007

Subjects
Primary: 33D20
Secondary: 33D45: Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.)

Citation

Spiridonov, Vyacheslav; Zhedanov, Alexei. Zeros and orthogonality of the Askey-Wilson polynomials for $q$ a root of unity. Duke Math. J. 89 (1997), no. 2, 283--305. doi:10.1215/S0012-7094-97-08914-6. https://projecteuclid.org/euclid.dmj/1077241019


Export citation

References

  • [1] W. Al-Salam, W. R. Allaway, and R. Askey, Sieved ultraspherical polynomials, Trans. Amer. Math. Soc. 284 (1984), no. 1, 39–55.
  • [2] R. Askey and J. Wilson, A set of orthogonal polynomials that generalize the Racah coefficients or $6-j$ symbols, SIAM J. Math. Anal. 10 (1979), no. 5, 1008–1016.
  • [3] R. Askey and J. Wilson, Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials, Mem. Amer. Math. Soc. 54 (1985), no. 319, iv+55.
  • [4] F. V. Atkinson, Discrete and continuous boundary problems, Mathematics in Science and Engineering, vol. 8, Academic Press, New York, 1964.
  • [5] E. Bannai and T. Ito, Algebraic combinatorics. I, The Benjamin/Cummings Publishing Co. Inc., Menlo Park, CA, 1984.
  • [6] R. D. Carmichael, The general theory of linear $q$-difference equations, Amer. J. Math. 34 (1912), 147–168.
  • [7] K. Chandrasekharan, Introduction to Analytic Number Theory, Die Grundlehren der mathematischen Wissenschaften, Band 148, Springer-Verlag New York Inc., New York, 1968.
  • [8] T. S. Chihara, An introduction to orthogonal polynomials, Gordon and Breach Science Publishers, New York, 1978.
  • [9] G. Gasper and M. Rahman, Basic hypergeometric series, Encyclopedia of Mathematics and its Applications, vol. 35, Cambridge University Press, Cambridge, 1990.
  • [10] D. Gupta and D. Masson, Contiguous relations, continued fractions and orthogonality, to appear in Trans. Amer. Math. Soc.
  • [11] M. E. H. Ismail and M. Rahman, The associated Askey-Wilson polynomials, Trans. Amer. Math. Soc. 328 (1991), no. 1, 201–237.
  • [12] R. Koekoek and R. F. Swarttouw, The Askey scheme of hypergeometric orthogonal polynomials and its $q$-analog 94-05, Delft Univ., 1994.
  • [13] N. M. Korobov, Exponential sums and their applications, Mathematics and its Applications (Soviet Series), vol. 80, Kluwer Academic Publishers Group, Dordrecht, 1992.
  • [14] D. A. Leonard, Orthogonal polynomials, duality and association schemes, SIAM J. Math. Anal. 13 (1982), no. 4, 656–663.
  • [15] A. F. Nikiforov, S. K. Suslov, and V. B. Uvarov, Classical orthogonal polynomials of a discrete variable, Springer Series in Computational Physics, Springer-Verlag, Berlin, 1991.
  • [16] V. Spiridonov and A. Zhedanov, Discrete Darboux transformations, the discrete-time Toda lattice, and the Askey-Wilson polynomials, Methods Appl. Anal. 2 (1995), no. 4, 369–398.
  • [17] V. Spiridonov and A. Zhedanov, $q$-ultraspherical polynomials for $q$ a root of unity, Lett. Math. Phys. 37 (1996), no. 2, 173–180.
  • [18] M. W. Wilson, On a new discrete analogue of the Legendre polynomials, SIAM J. Math. Anal. 3 (1972), 157–169.