Chebyshev polynomials on circular arcs

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3 Citations (Scopus)


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 languageEnglish
Pages (from-to)629-649
Number of pages21
JournalActa Scientiarum Mathematicarum
Issue number3-4
Publication statusPublished - 2019


  • Chebyshev polynomials
  • Circular arc
  • Jacobian elliptic function
  • Jacobian theta function


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