Abstract
The present paper is a continuation of our paper [4]. The problem to be studied is the non-impact of algebraic property on the convergence properties of the mu-th root base of special monogenic polynomials. These convergence properties are the investigation of the relation between the effectiveness in closed balls of a given base and that of its mu-th root base, and also the relation between their rate of increase. Our result which is concerned with effectiveness in closed balls is quite different from its corresponding one for the square root case in complex settings.