Algebraic Independence by Approximation Method (II)

Let f (x) be a continued fraction with elements a n x, where coefficients a n are positive algebraic numbers. Using the criterion of [l] for any nonzero real algebraic numbers .1,...,.s with distinct absolute values the algebraic independence of the values f(.1), ..., f(.s) is proved under certain assumption concerning only with a n . For some transcendental numbers . the algebraic independence of values f(.j)(j..) is also established.