Polynomial approximation of conformal maps (Q1381492)

Let \(G\) be a Jordan domain bounded by a piecewise-analytic curve \(\Gamma\) without cusps, and let \(f\) be a conformal map of \(G\) onto the unit disk. By use of the ``Lehman formulas'' for the asymptotic expansion of mapping functions near analytic corners (see R. S. Lehman [Pac. J. Math. 7, 1437-1449 (1957; Zbl 0087.28902)]) the author improves own results [Constructive Approximation 4, No. 3, 289-305 (1988; Zbl 0645.30002) and Arch. Math. 58, No. 5, 462-470 (1992; Zbl 0756.30005)]. He obtains sharper estimates of the best rate of uniform approximation of \(f\) by polynomials and the rate of convergence of Bieberbach polynomials to \(f\) for the special case that the corners of \(\Gamma\) have interior angles of the form \({\pi\over N}\), \(N\in\mathbb{N}\).