Algebraic Independence by Approximation Method (II)

Let f (x) be a continued fraction with elements anx, where coefficients anare positive algebraic numbers. Using the criterion of [l] for any nonzero real algebraic numbers α1,...,αs with distinct absolute values the algebraic independence of the values f(α1), ..., f(αs) is proved under certain assumption concerning only with an. For some transcendental numbers ξ the algebraic independence of values f(ξj)(j∈ℤ) is also established.