# Polynomials orthogonal on the semicircle, II

@article{Gautschi1987PolynomialsOO,
title={Polynomials orthogonal on the semicircle, II},
author={Walter Gautschi and Henry J. Landau and Gradimir V. Milovanovic},
journal={Constructive Approximation},
year={1987},
volume={3},
pages={389-404}
}
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
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