On a property of finite truncations of the Laurent series of analytic functions. (English) Zbl 0545.30016

Abian, Alexander

Publ. Math. Debr. 30, 129-131 (1983).

For the Laurent series \(\sum^{+\infty}_{-\infty}a_ m(z-a)^ m\) of an analytic function f at the isolated essential singularity a it is shown that there exists a sequence \((c_ n)\) such that the \(c_ n\) are zeros of finite truncations \(\sum^{p}_{-k}a_ m(z-a)^ m\) of the Laurent series from f such that \(\lim_{n\to \infty}f(c_ n)=0\) provided that O is not a Picard exceptional value from f.

Reviewer: J.Winkler

MSC:

30D10

Representations of entire functions of one complex variable by series and integrals

Keywords:

Laurent series; isolated essential singularity; finite truncations; Picard exceptional value