Algebraic Independence by Approximation Method(Ⅱ)

Let f(x)be a continued fraction with elements ax,where coefficients aare positive alge-braic numbers.Using the criterion of[1]for any nonzero real algebraic numbers α,...,αwith distinctabsolute values the algebraic independence of the values f(α),...,f(α)is proved under certain as-sumption concerning only with a.For some transcendental numbers ζ the algebraic independence ofvalues f(ζ~j)(j∈Z)is also established.