Geodesic
On Asymptotic Properties of Interpolation Polynomials
Matematičeskie zametki, Tome 83 (2008) no. 1, pp. 129-138

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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.
Mots-clés : interpolation polynomial, Hermite interpolation formula, Cauchy–Hadamard formula.
Keywords: Taylor series, holomorphic function 
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     author = {D. V. Khristoforov},
     title = {On {Asymptotic} {Properties} of {Interpolation} {Polynomials}},
     journal = {Matemati\v{c}eskie zametki},
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     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2008_83_1_a13/}
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D. V. Khristoforov. On Asymptotic Properties of Interpolation Polynomials. Matematičeskie zametki, Tome 83 (2008) no. 1, pp. 129-138. http://geodesic.mathdoc.fr/item/MZM_2008_83_1_a13/