Complex Kergin interpolation (Q1174318)

Let \(D\subset\mathbb{C}^ n\) be a domain whose intersection with any complex line be either empty or a simply connected domain in \(\mathbb{C}\). Given \(m+1\) points \(p_ 0,p_ 1,\dots,p_ m\) in \(D\), then for each \(f\in{\mathcal O}(D)\) a polynomial \(q_ m(z)\) of degree \(m\) is constructed, who interpolates \(f\) at \(p_ 0,p_ 1,\dots,p_ m\). Hermite interpolating formula for the remainder \(f-q_ m\) is given. The result is a generalization of the corresponding result of Kergin concerning interpolation in \(\mathbb{R}^ n\).