On Faber polynomials generated by an $m$-star

The zeros of Faber polynomials generated by an m-star

It is shown that the zeros of the Faber polynomials generated by a regular m-star are located on the m-star. This proves a recent conjecture of J. Bartolomeo and M. He. The proof uses the connection between zeros of Faber polynomials and Chebyshev quadrature formulas.

Coefficient Estimates for a General Subclass of m-fold Symmetric Bi-univalent Functions by Using Faber Polynomials

In the present paper, we introduce a new subclass H∑m (λ,β)of the m-fold symmetric bi-univalent functions. Also, we find the estimates of the Taylor-Maclaurin initial coefficients |am+1| , |a2m+1| and general coefficients |amk+1| (k ≥ 2) for functions in this new subclass. The results presented in this paper would generalize and improve some recent works of several earlier authors.

Lattice Paths and Faber Polynomials

The rth Faber polynomial of the Laurent series f(t) = t + f0 + f1/t + f2/t + · · · is the unique polynomial Fr(u) of degree r in u such that Fr(f) = tr + negative powers of t. We apply Faber polynomials, which were originally used to study univalent functions, to lattice path enumeration.

The Faber Polynomials for Circular Sectors

The Faber polynomials for a region of the complex plane, which are of interest as a basis for polynomial approximation of analytic functions, are determined by a conformai mapping of the complement of that region to the complement of the unit disc. We derive this conformai mapping for a circular sector {;: \z\ < 1, |argz| < i/a}, where a > 1, and obtain a recurrence relation for the coefficient...

Faber Polynomials for Rational Mapping Functions