Polynomials orthogonal on the semicircle, II

  title={Polynomials orthogonal on the semicircle, II},
  author={Walter Gautschi and Henry J. Landau and Gradimir V. Milovanovic},
  journal={Constructive Approximation},
AbstractGeneralizing previous work [2], we study complex polynomials {πk},πk(z)=zk+⋯, orthogonal with respect to a complex-valued inner product (f,g)=∫0πf(eiθ)g(eiθ)w(eiθ)dθ. Under suitable assumptions on the “weight function”w, we show that these polynomials exist whenever Re ∫0πw(eiθ)dθ≠0, and we express them in terms of the real polynomials orthogonal with respect to the weight functionw(x). We also obtain the basic three-term recurrence relation. A detailed study is made of the polynomials… CONTINUE READING


Publications referenced by this paper.

Gautschi , Jet Wimp ( to appear ) : Computing the Hilbert transform of a Jacobi weight function

J. M. Boyle, J. J. Dongarra, +3 authors C. B. Moler
  • Matrix Eigensystem Routines - - EISPACK Guide
  • 1976

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