Explicit representations of Faber polynomials for \(m\)-cusped hypocycloids (Q1125964)

This is a continuation of an earlier study by the same author and \textit{E. B. Saff} [J. Approximation Theory 78, No. 3, 410-432 (1994; Zbl 0814.41006)]. Let \(H_m\) denote the hypocycloid generated by the function \(\psi(w)= w+(m-1)^{-1} w^{1-m}\), \(m=2,3, \dots\) and let \(F_n(z)\) be the Faber polynomial of degree \(n\) associated with \(H_m\). By means of the Cauchy integral formula the author gives here an explicite formula for \(F_n(z)\). Then he derives a representation of \(F_n(z)\) in terms of hypergeometric functions \((m=3)\) and, in the case of an \(m\)-cusped hypercycloid, \(m\geq 3\), in terms of generalized hypergeometric functions.