Representations of analytic functions on typical domains in terms of local values and truncation error estimates. (Q2749814)

This article is a continuation of a paper by \textit{S. Saitoh} and \textit{M. Mori} [Complex Variables, Theory Appl. 45, No. 4, 387--393 (2001; Zbl 1022.30008)]. In that paper the authors gave a series expansion for an analytic function \(f\) defined in a non-degenerate simply-connected domain \(D\) on the complex plane with \(0\in D\). The expansion holds for all \(z\in D\) and its coefficients are expressed in terms of the Taylor coefficients of the Riemann map onto \(D\) and of the Taylor coefficients of \(f\) around \(0\). In the paper under review the authors provide some examples of specific domains for which the expansion is applied and give concrete represantation formulas and truncation error estimates.NEWLINENEWLINEFor the entire collection see [Zbl 0963.00016].