Polynomials orthogonal on the semicircle
type: Item
instance of: scholarly article
title: Polynomials orthogonal on the semicircle
zbMATH Open document ID: 0604.42024
DOI: 10.1016/0021-9045(86)90064-X
author: Walter Gautschi
author: Gradimir V. Milovanović
published in: Journal of Approximation Theory
publication date: 1986-01-01T00:00:00Z
review text: The authors study the complex polynomials \(\{\pi_ n\}\) which are orthogonal with respect to the complex-valued inner product \((f,g)=\int^{\pi}_{0}f(e^{i\theta})g(e^{i\theta})d\theta.\) For these polynomials, they obtain a three-term recurrence relation, a linear differential equation of second order and discuss the nature of the zeros. A relationship between these polynomials and the Legendre polynomials is worked out. Finally, they discuss some interesting applications of these polynomials.
Mathematics Subject Classification ID: 42C05
Mathematics Subject Classification ID: 33C45
Mathematics Subject Classification ID: 33C55
Mathematics Subject Classification ID: 30C15
zbMATH DE Number: 3975573
zbMATH Keywords: complex polynomials
zbMATH Keywords: recurrence relation
zbMATH Keywords: linear differential equation of second order
zbMATH Keywords: Legendre polynomials
zbMATH Keywords: applications
Wikidata QID: Q115058829
reviewed by: Ajendra Nath Srivastava
describes a project that uses: EISPACK
describes a project that uses: LINPACK
describes a project that uses: FUNPACK
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3975573