On Some Polynomials with Weighted Sums

Abstract

In this note, we study a generalization of a certain polynomial $z^n-{\sum\limits_{k=0}^{n-1}}a_kz^k$ 수식 이미지, where $\sum\limits_{k=0}^{n-1}a_k=1$ 수식 이미지, $a_k{\geq}0$ 수식 이미지 for each k, whose all zeros except for z=1 lie on the circle of radius 1/2 with center at the origin