On zeros of the regular power series of a quaternionic variable

Using tools from the newly developed theory of regular functions and polynomials with quaternionic coefficients located on only one side of the variable, we derive zero-free regions for the related subclass of regular power series and obtain discs that are not centered at the origin, containing all the zeros of these polynomials. The results obtained for this particular subclass of regular functions lead to generalizations of several results that are known from the relevant literature.