Abstract
A series of Stieltjes is a (formal) power series f ( z ) = ~ ~ e.(-z) where e.=fo tde(t) for some real, bounded, nondecreasing function e(t) assuming infinitely many values on t~0. These functions were first studied by Stieltjes who proved that the moment problem on [0, ~[ associated with {e.}~= 0 is determinate if and only if the corresponding continued fractions expansion off(z) converges except on the negative real axis. (Stieltjes [10].) This theorem is also of significance for the theory of Pad4 approximation (Pad4 [8]),
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