Abstract
In this paper, we study the asymptotic properties of the polynomials P n (z) = P n (z; f), corresponding to an interpolation table α ⊂ E, where E is a bounded continuum in the complex plane with a connected complement, the table α 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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Original Russian Text © D. V. Khristoforov, 2008, published in Matematicheskie Zametki, 2008, Vol. 83, No. 1, pp. 129–138.
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Khristoforov, D.V. On asymptotic properties of interpolation polynomials. Math Notes 83, 116–124 (2008). https://doi.org/10.1134/S0001434608010148
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DOI: https://doi.org/10.1134/S0001434608010148