Abstract:
In this paper, we study the asymptotic properties of the polynomials $P_n(z)=P_n(z;f)$, corresponding to an interpolation table $\alpha\subset E$, where $E$ is a bounded continuum in
the complex plane with a connected complement, the table $\alpha$ satisfies the Kakehashi condition, and $f$ is an arbitrary function holomorphic on $E$. In particular, for zeros of such polynomials, we obtain a generalization of the classical Jentzsch–Szegő theorem on the distribution of zeros of partial sums of Taylor series.
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