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Computational Methods and Function Theory 9 (2009), No. 1, 305--322
Copyright Heldermann Verlag 2009

On the Stability of Taylor Sections of a Function Σk=0∞ zk/ak2, a>1

Olga M. Katkova
olga.m.katkova@univer.kharkov.ua , Kharkov National University, Dept. of Math., Svobody sq., 4, 61077, Kharkov, Ukraine.

Anna M. Vishnyakova
anna.m.vishnyakova@univer.kharkov.ua , Kharkov National University, Dept. of Math., Svobody sq., 4, 61077, Kharkov, Ukraine.

[Abstract-pdf] [Abstract-ps]

We investigate the following problem: given a positive integer n, which are the smallest values of the constants sn, such that the zeros of fa,n(z) := Σk=0∞ zk/ak2 are with negative real parts when a>sn?

Keywords: Hurwitz polynomial, stable polynomial, zeros of sections of entire functions.

MSC 2000: 30C15, 30D15, 26C10, 34D99.

[FullText-pdf (318 K)] [FullText-ps (545 K)]