Explicit Faber polynomials on circular sectors

Authors:
Karin Gatermann, Christoph Hoffmann and Gerhard Opfer

Journal:
Math. Comp. **58** (1992), 241-253, 51

MSC:
Primary 30C10; Secondary 30-04, 30C20, 65A05

MathSciNet review:
1106967

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Abstract: We present explicit and precise expressions for the Faber polynomials on circular sectors up to degree 20. The precision is obtained by modifying (and simultaneously speeding up) an algorithm of Coleman and Smith so that an essential part of the Faber polynomials can be represented using only rational numbers. The growth of the coefficients of the Faber polynomials is determined. In addition, explicit expressions are given for the area two-norm and line two-norm of these polynomials. A conjecture is stated with respect to the uniform (infinity) norm which would also allow the explicit computation of the corresponding uniform norms of the Faber polynomials. Apart from a table of Faber polynomials, there are several other tables and graphs that illustrate the behavior of the Faber polynomials.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1992-1106967-4

Keywords:
Faber polynomials,
circular sectors,
outer conformal mapping of sectors

Article copyright:
© Copyright 1992
American Mathematical Society