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Diophantine approximation of Mahler numbers

Suppose that F(x)∈Z[[x]] is a Mahler function and that 1/b is in the radius of convergence of F(x) for an integer b⩾2 . In this paper, we consider the approximation of F(1/b) by algebraic numbers. In particular, we prove that F(1/b) cannot be a Liouville number. If, in addition, F(x) is regular, we show that F(1/b) is either rational or transcendental, and in the latter case that F(1/b) is an S ‐number or a T ‐number in Mahler's classification of real numbers.