Computational Methods and Function Theory 4 (2004), No. 2, 275--282
Copyright Heldermann Verlag 2004
Iossif V. Ostrovskii
iossif@fen.bilkent.edu.tr , Department of Mathematics, Bilkent University, 06800 Bilkent, Ankara, Turkey; Institute for Low Temperature Physics and Engineering, 47 Lenin ave, 61103 Kharkov, Ukraine.
Let $P_{mn}$, $0< m< n-1$, 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 $m,n\to\infty$ in such a way that $\lim_{m,n\to\infty}m/n=\alpha\in(0,1)$, then the zeros of $P_{mn}$ tend to a curve which can be explicitly described.
Keywords: Asymptotic formula, conformal mapping, polynomial, subharmonic function, Szegö's method, univalent function, zeros.
MSC 2000: 26C10, 30C15.
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