## On Faber polynomials generated by an $m$-star

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- by J. Bartolomeo and Matthew He PDF
- Math. Comp.
**62**(1994), 277-287 Request permission

## Abstract:

In this paper, we study the Faber polynomials ${F_n}(z)$ generated by a regular*m*-star $(m = 3,4, \ldots )$ \[ {S_m} = \{ {x{\omega ^k};0 \leq x \leq {4^{1/m}},k = 0,1, \ldots ,m - 1,{\omega ^m} = 1} \}.\] An explicit and precise expression for ${F_n}(z)$ is obtained by computing the coefficients via a Cauchy integral formula. The location and limiting distribution of zeros of ${F_n}(z)$ are explored. We also find a class of second-order hypergeometric differential equations satisfied by ${F_n}(z)$. Our results extend some classical results of Chebyshev polynomials for a segment $[ - 2,2]$ in the case when $m = 2$.

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## Additional Information

- © Copyright 1994 American Mathematical Society
- Journal: Math. Comp.
**62**(1994), 277-287 - MSC: Primary 30C45; Secondary 41A58
- DOI: https://doi.org/10.1090/S0025-5718-1994-1203732-6
- MathSciNet review: 1203732