On Faber Polynomials Generated by an m-star

J. Bartolomeo; Matthew He

doi:10.1090/S0025-5718-1994-1203732-6

On Faber Polynomials Generated by an m-star

J. Bartolomeo
, Matthew He

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

12 Scopus citations

Abstract

In this paper, we study the Faber polynomials generated by a regular m -star

An explicit and precise expression for is obtained by computing the coefficients via a Cauchy integral formula. The location and limiting distribution of zeros of are explored. We also find a class of second-order hypergeometric differential equations satisfied by . Our results extend some classical results of Chebyshev polynomials for a segment in the case when .

Original language	American English
Pages (from-to)	277-287
Journal	Mathematics of Computation
Volume	62
DOIs	https://doi.org/10.1090/S0025-5718-1994-1203732-6
State	Published - Jan 1 1994

Keywords

Faber polynomials
Zero distribution
m-star

Disciplines

Mathematics

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http://www.ams.org/journals/mcom/1994-62-205/S0025-5718-1994-1203732-6/S0025-5718-1994-1203732-6.pdf

Cite this

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abstract = " In this paper, we study the Faber polynomials generated by a regular m -star An explicit and precise expression for is obtained by computing the coefficients via a Cauchy integral formula. The location and limiting distribution of zeros of are explored. We also find a class of second-order hypergeometric differential equations satisfied by . Our results extend some classical results of Chebyshev polynomials for a segment in the case when .",

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AU - He, Matthew

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N2 - In this paper, we study the Faber polynomials generated by a regular m -star An explicit and precise expression for is obtained by computing the coefficients via a Cauchy integral formula. The location and limiting distribution of zeros of are explored. We also find a class of second-order hypergeometric differential equations satisfied by . Our results extend some classical results of Chebyshev polynomials for a segment in the case when .

AB - In this paper, we study the Faber polynomials generated by a regular m -star An explicit and precise expression for is obtained by computing the coefficients via a Cauchy integral formula. The location and limiting distribution of zeros of are explored. We also find a class of second-order hypergeometric differential equations satisfied by . Our results extend some classical results of Chebyshev polynomials for a segment in the case when .

KW - Faber polynomials

KW - Zero distribution

KW - m-star

UR - https://nsuworks.nova.edu/math_facarticles/196

UR - http://www.ams.org/journals/mcom/1994-62-205/S0025-5718-1994-1203732-6/S0025-5718-1994-1203732-6.pdf

U2 - 10.1090/S0025-5718-1994-1203732-6

DO - 10.1090/S0025-5718-1994-1203732-6

M3 - Article

SN - 0025-5718

VL - 62

SP - 277

EP - 287

JO - Mathematics of Computation

JF - Mathematics of Computation

ER -

On Faber Polynomials Generated by an m-star

Abstract

Keywords

Disciplines

Access to Document

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