The convergence of Padé approximants to series of Stieltjes
The convergence of Padé approximants to series of Stieltjes
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 …