On Mahler’s S-numbers, T-numbers, and U-numbers

In this work, we consider some power series with algebraic coefficients from a certain algebraic number field, whose radiuses of convergence are infinite. We show that under certain conditions these series take transcendental values at non-zero algebraic number arguments, and we determine the classes to which these transcendental values belong in Mahler`s classification. Then we consider these series for certain Liouville number arguments and obtain similar results.