Abstract
(3) a2n =A21(BnBn_-) a2n+l =B2/(AnAn+ ) . Conversely, the positive real numbers ai (i = 1, 2, 3, ) uniquely determine coefficients ci of a Stieltjes power series. Thus to every Stieltjes continued fraction (2) with positive ai there corresponds a Stieltjes series (1) and vice versa. In the work of Stieltjes the convergents of (2) separate into two sets, the odd and the even convergents. When the seriest Zai is divergent, these
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