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PC-fractions and Szegö polynomials associated with starlike univalent functions

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Abstract

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.

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

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Keywords

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