Polynomials orthogonal on the semicircle. II
type: Item
instance of: scholarly article
title: Polynomials orthogonal on the semicircle. II
zbMATH Open document ID: 0658.42027
DOI: 10.1007/BF01890577
author: Walter Gautschi
author: Henry Landau
author: Gradimir V. Milovanović
published in: Constructive Approximation
publication date: 1987-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 42C05
Mathematics Subject Classification ID: 33E99
Mathematics Subject Classification ID: 33C45
zbMATH DE Number: 4075756
zbMATH Keywords: three term recurrence relations
zbMATH Keywords: zeros
zbMATH Keywords: Jacobi weight function
zbMATH Keywords: Gegenbauer weight functions
Wikidata QID: Q115058822
reviewed by: Ajendra Nath Srivastava
describes a project that uses: EISPACK
MaRDI profile type: Publication
cites work: Some Elementary Inequalities Relating to the Gamma and Incomplete Gamma Function
cites work: Polynomials orthogonal on the semicircle
cites work: Matrix eigensystem routines - EISPACK guide. 2nd ed
full work available at URL: https://doi.org/10.1007/bf01890577
OpenAlex ID: W2015017128
description: scientific article; zbMATH DE number 4075756