Transcendental numbers in fields of formal power series

Mahler divided the real transcendental numbers into three disjoint classes. Bundschuh carried over this classification to the field K of formal power series over a finite field K and introduced a similar classification. So he separated transcendental formal power series into three disjoint classes. U−numbers are one of these classes. U−numbers are subdivided into Um−subclasses (m = 1,2, . . . ). We work on Um−numbers in the field K. Firstly, we establish a result which enables us to construct explicit examples of Um−numbers by using continued fraction expansions of algebraic formal power series of degree m in K. Next, we show that the values of some polynomials whose coefficients belong to a field extension of degree m over K(x) at some U1−numbers in K are Um−numbers.