On a Problem of A. Eremenko
Date
2005-05
Authors
Ostrovskii, I. V.
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Abstract
Let Pmn, 0 < m < n− 1, be a polynomial formed by the first m terms of the expansion of (1 + z)n according to the binomial formula. We show that, if m, n→∞ in such a way that limm,n→∞ m/n = α ∈ (0, 1), then the zeros of Pmn tend to a curve which can be explicitly described.
Source Title
Computational Methods and Function Theory
Publisher
Springer
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Keywords
Asymptotic formula, Conformal mapping, Polynomial, Subharmonic function, Szego’s method, Univalent function, Zeros
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English