Polynomials orthogonal on the semicircle. II
The authors continue their study of polynomials which are orthogonal on the semi circle. The present paper generalizes their previous work [see Part I of this work, J. Approximation Theory 46, 230-250 (1986; Zbl 0604.42024)]. Here study is made of complex polynomials \(\{\pi_ k\}\), \(\pi_ k=z^ k+...\), orthogonal with respect to the inner product: \((f,g) = \int^{\pi}_{0} f(e^{i\theta}) g(e^{i\theta}) w(e^{i\theta})d\theta\). Two special forms of the polynomials \(\{\pi_ k\}\) in the cases of Jacobi and Gegenbauer weight functions are discussed in length. This part is also of excellent contents and is well-written.
scientific article; zbMATH DE number 4075756