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

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