Borel-Pade vs Borel-Weniger method: a QED and a QCD example

Abstract

Recently, Weniger (delta sequence) method has been proposed by the authors of Ref. [1] (Jentschura et al.) for resummation of truncated perturbation series in quantum field theories. Those authors presented numerical evidence suggesting that this method works better than Pade approximants when we resum a function with singularities in the Borel plane but not on the positive axis. We present here numerical evidence suggesting that in such cases the combined method of Borel-Pade works better than its analog Borel-Weniger, and that it may work better or comparably well in some of the cases when there are singularities on the positive axis in the Borel plane.