Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

PC-fractions and Szegö polynomials associated with starlike univalent functions

  • 47 Accesses

  • 1 Citations


Each classS α, 0≤α<1, functions starlike of order α, can be associated with a Carathéodory function mapping the unit disk onto a subset of the right halfplane. This Carathéodory function determines a certain continued fraction (PC-fraction) and a family of polynomials orthogonal on the unit circle (Szegö polynomials). We compute the PC-fraction and Szegö polynomials corresponding to eachS α and do some investigations on these PC-fractions and Szegö polynomials.

This is a preview of subscription content, log in to check access.


  1. [1]

    P.L. Duren,Univalent Functions (Springer, New York, 1983).

  2. [2]

    A.W. Goodman,Univalent Functions (Mariner, Tampa, Fl., 1983).

  3. [3]

    W.B. Jones and O. Njåstad, Applications of Szegö polynomials to digital signal processing, Rocky Mountain J. Math. 21 (1991) 387–436.

  4. [4]

    W.B. Jones, O. Njåstad and W.J. Thron, Continued fractions associated with trigometric and other strong moment problems, Constr. Appr. 2 (1986) 197–211.

  5. [5]

    W.B. Jones, O. Njåstad and W.J. Thron, Schur fractions, Perron-Carathéodory fractions and Szegö polynomials, a survey,Analytic Theory of Continued Fractions II, ed. W.J. Thron, Lecture Notes in Math. 1199 (Springer, 1986) pp. 127–158.

  6. [6]

    W.B. Jones, O. Njåstad and E.B. Saff, Szegö polynomials associated with Wiener-Levinson filters, J. Comp. Appl. Math. 32 (1990) 387–406.

  7. [7]

    M.S. Robertson, On the theory of univalent functions, Ann. Math. 32 (1936) 374–408.

Download references

Author information

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Rønning, F. PC-fractions and Szegö polynomials associated with starlike univalent functions. Numer Algor 3, 383–391 (1992). https://doi.org/10.1007/BF02141945

Download citation


  • Unit Circle
  • Unit Disk
  • Univalent Function
  • Continue Fraction
  • Starlike Univalent Function