The Faber polynomials for circular lunes
type: Item
instance of: scholarly article
title: The Faber polynomials for circular lunes
zbMATH Open document ID: 0836.30024
DOI: 10.1016/0898-1221(95)00109-3
publication date: 1995-12-18T00:00:00Z
review text: Let \(D_\alpha\) be the circular lune symmetric with respect to both axis with vertices at \(z = \pm \alpha\) and exterior angle \(\alpha \pi\), \(0 < \alpha \leq 2\). Let \(z = \psi (w) = w + \sum^\infty_{k = 0} b_k w^{-k}\) map \(\{w : |w |> 1\}\) conformally onto the exterior of \(D_\alpha\). The author determines explicitly \(\psi\), its coefficients \(b_k\), and the Faber polynomials \(F_n\) for the set \(D_\alpha\). The zeros of \(F_n\) and of \(F_n'\) are determined as eigenvalues of two matrices involving the \(b_k\), and these are computed for \(\alpha = {1 \over 2}\) and \(\alpha = {3 \over 2}\), for \(n = 30\) and \(n = 31\). The experiments suggest that the zeros of \(F_n\) and of \(F_n'\) are all inside \(D_\alpha\) and are `interlacing'.
Mathematics Subject Classification ID: 30E10
Mathematics Subject Classification ID: 30C10
zbMATH DE Number: 826979
zbMATH Keywords: Faber polynomials
author: Matthew He
reviewed by: Dieter Gaier
MaRDI profile type: Publication
full work available at URL: 0898-1221(95)00109-3
OpenAlex ID: W1975422646
cites work: Computation of Faber Series With Application to Numerical Polynomial Approximation in the Complex Plane
cites work: The Faber Polynomials for Circular Sectors
cites work: Explicit Faber Polynomials on Circular Sectors
cites work: A numerical method for the computation of Faber polynomials for starlike domains
cites work: The zeros of Faber polynomials for an \(m\)-cusped hypocycloid
cites work: Zeros and local extreme points of Faber polynomials associated with hypocycloidal domains
cites work: Q4283206
cites work: The Faber polynomials for \(m\)-fold symmetric domains
cites work: On Faber Polynomials Generated by An m-Star
cites work: The Location of the Zeros of the Derivatives of Faber Polynomials
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 826979