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1: 18.33 Polynomials Orthogonal on the Unit Circle
§18.33 Polynomials Orthogonal on the Unit Circle
§18.33(i) Definition
§18.33(ii) Recurrence Relations
For an alternative and more detailed approach to the recurrence relations, see §18.33(vi). …
§18.33(iv) Special Cases
2: 15.1 Special Notation
3: Bibliography S
  • B. Simon (2005a) Orthogonal Polynomials on the Unit Circle. Part 1: Classical Theory. American Mathematical Society Colloquium Publications, Vol. 54, American Mathematical Society, Providence, RI.
  • B. Simon (2005b) Orthogonal Polynomials on the Unit Circle. Part 2: Spectral Theory. American Mathematical Society Colloquium Publications, Vol. 54, American Mathematical Society, Providence, RI.
  • A. Sri Ranga (2010) Szegő polynomials from hypergeometric functions. Proc. Amer. Math. Soc. 138 (12), pp. 4259–4270.
  • G. Szegő (1975) Orthogonal Polynomials. 4th edition, Colloquium Publications, Vol. XXIII, American Mathematical Society, Providence, RI.
  • 4: Bibliography
  • W. A. Al-Salam and M. E. H. Ismail (1994) A q -beta integral on the unit circle and some biorthogonal rational functions. Proc. Amer. Math. Soc. 121 (2), pp. 553–561.
  • R. Askey (1982a) Commentary on the Paper “Beiträge zur Theorie der Toeplitzschen Form”. In Gábor Szegő, Collected Papers. Vol. 1, Contemporary Mathematicians, pp. 303–305.
  • 5: Bibliography Z
  • A. Zhedanov (1998) On some classes of polynomials orthogonal on arcs of the unit circle connected with symmetric orthogonal polynomials on an interval. J. Approx. Theory 94 (1), pp. 73–106.
  • 6: Bibliography P
  • P. I. Pastro (1985) Orthogonal polynomials and some q -beta integrals of Ramanujan. J. Math. Anal. Appl. 112 (2), pp. 517–540.
  • 7: 15.2 Definitions and Analytical Properties
    8: 17.4 Basic Hypergeometric Functions
    9: Bibliography H
  • E. Hendriksen and H. van Rossum (1986) Orthogonal Laurent polynomials. Nederl. Akad. Wetensch. Indag. Math. 48 (1), pp. 17–36.
  • 10: 17.2 Calculus