Finding the areas of convergence and calculating the sums of power series of an h-complex variable

Abstract

Herein, taking power series from a real variable that converge on a certain interval to known sums, the authors consider the power series with the same coefficients from an h-complex variable. For such series, the interiors of the regions of convergence are found, and their sums are explicitly expressed in terms of the sums of the original series. Along the way, the problem of isolation conditions for the zeros of the sums of such series is solved.