Mathematics Faculty Articles

Title

The Faber Polynomials for Circular Lunes

Document Type

Article

Publication Date

9-1-1995

Publication Title

Computers & Mathematics with Applications

Keywords

Conformal mapping, Faber polynomial, Circular lune

ISSN

0898-1221

Volume

30

Issue/No.

3-6

First Page

307

Last Page

315

Abstract

We study the Faber polynomials Fn(z) generated by a circular lune symmetric about both axes with vertices at the points z = ±α (0 < α ≤ 2) and exterior angle απ. An explicit expression of Fn(z) was obtained by computing the coefficients via a Cauchy integral formula. We also illustrate the location of the zeros of Faber polynomial and of its derivative. Our results include a circle and a segment as special cases when α = 1, 2, respectively.

DOI

10.1016/0898-1221(95)00109-3

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