Abstract
We consider a class of functionsF(z) for which a formal expansion in power ofz gives a Stieltjes series with divergent moments. We show that, introducing a proper cut-off for the moments, we can sum such a series in the framework of the Pade-approximant method, through a connection between the limit on the order of the approximants and the limit on the cut-off. Due to this connection, for which we give some general rules, it is possible to obtain rapidly converging approximations toF(z), starting from the knowledge of the first terms of the formal series.
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