Chebyshev polynomials on circular arcs

Klaus Schiefermayr

doi:10.14232/actasm-018-343-y

Chebyshev polynomials on circular arcs

Klaus Schiefermayr

Research Center Wels

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

3 Citations (Scopus)

Abstract

In this paper, we give an explicit representation of the complex Chebyshev polynomials on a given arc of the unit circle (in the complex plane) in terms of real Chebyshev polynomials on two symmetric intervals (on the real line). The real Chebyshev polynomials, for their part, can be expressed via a conformal mapping with the help of Jacobian elliptic and theta functions, which goes back to the work of Akhiezer in the 1930's.

Original language	English
Pages (from-to)	629-649
Number of pages	21
Journal	Acta Scientiarum Mathematicarum
Volume	85
Issue number	3-4
DOIs	https://doi.org/10.14232/actasm-018-343-y https://doi.org/10.14232/actasm-018-343-y
Publication status	Published - 2019

Keywords

Chebyshev polynomials
Circular arc
Jacobian elliptic function
Jacobian theta function

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title = "Chebyshev polynomials on circular arcs",

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AB - In this paper, we give an explicit representation of the complex Chebyshev polynomials on a given arc of the unit circle (in the complex plane) in terms of real Chebyshev polynomials on two symmetric intervals (on the real line). The real Chebyshev polynomials, for their part, can be expressed via a conformal mapping with the help of Jacobian elliptic and theta functions, which goes back to the work of Akhiezer in the 1930's.

KW - Chebyshev polynomials

KW - Circular arc

KW - Jacobian elliptic function

KW - Jacobian theta function

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DO - 10.14232/actasm-018-343-y

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EP - 649

JO - Acta Scientiarum Mathematicarum

JF - Acta Scientiarum Mathematicarum

IS - 3-4

ER -

Chebyshev polynomials on circular arcs

Abstract

Keywords

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