Forms for meromorphic functions (Q1263228)

Circular arithmetic, which was introduced by \textit{I. Gargantini} and \textit{P. Henrici} [Numer. Math. 18, 305-320 (1972; Zbl 0228.65038)], and the suitably adapted concept of centered forms is extended here to power series and quotients of power series. A variety of quadratically convergent forms for meromorphic functions are obtained in this way. The circular complex centered forms are shown to provide including chains in general, whereas the power-sum forms have this property only under some restrictive conditions. Explicit representations are given both for the first few power-sum and centered forms.