古典的Enestrom-Kakeya定理指出:如果p(z)=∑mi=0aizi是一个形如0 ≤a0 ≤ a1≤a2≤…≤ an的多项式,则p(z)的所有零点都落在|z|≤1的复平面区域内.多项式的系数加上多种限制条件后(如,系数模的单调性),就存在很多的Enestrom-Kakeya推广的定理.本文中,将介绍当加上Z的偶次幂项和奇次幂项的系数条件限制后的一些结果.%The classical Enestrom-Kakeya Theorem states that if p(z) = ∑mn=0 avzv is a polynomial [z| ≤ 1 in the complex plane. Many generalizations of the Enestrom-Kakeya Theorem exist which put various conditions on the coefficients of the polynomial (such as mononicity of the moduli of the coefficients). In this paper, we will introduce several results which put conditions on the coefficients of even powers of Z and on the coefficients of odd powers of Z.As a consequence, our results will be applicable to some analytic functions to which these related results are not applicable.
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