The Faber Polynomials for Circular Lunes

Matthew He

doi:10.1016/0898-1221(95)00109-3

The Faber Polynomials for Circular Lunes

Matthew He

Research output: Contribution to journal › Article › peer-review

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Abstract

We study the Faber polynomials F n ( 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 F n ( 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.

Original language	American English
Pages (from-to)	307-315
Journal	Computers & Mathematics with Applications
Volume	30
Issue number	3-6
DOIs	https://doi.org/10.1016/0898-1221(95)00109-3
State	Published - Sep 1 1995

Keywords

Circular lune
Conformal mapping
Faber polynomial

Disciplines

Mathematics

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title = "The Faber Polynomials for Circular Lunes",

abstract = " We study the Faber polynomials F n ( 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 F n ( 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.",

keywords = "Circular lune, Conformal mapping, Faber polynomial",

author = "Matthew He",

year = "1995",

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T1 - The Faber Polynomials for Circular Lunes

AU - He, Matthew

PY - 1995/9/1

Y1 - 1995/9/1

N2 - We study the Faber polynomials F n ( 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 F n ( 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.

AB - We study the Faber polynomials F n ( 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 F n ( 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.

KW - Circular lune

KW - Conformal mapping

KW - Faber polynomial

UR - https://nsuworks.nova.edu/math_facarticles/190

U2 - 10.1016/0898-1221(95)00109-3

DO - 10.1016/0898-1221(95)00109-3

M3 - Article

SN - 0898-1221

VL - 30

SP - 307

EP - 315

JO - Computers & Mathematics with Applications

JF - Computers & Mathematics with Applications

IS - 3-6

ER -

The Faber Polynomials for Circular Lunes

Abstract

Keywords

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