0 Borel – Padé vs Borel – Weniger method : a QED and a QCD example

Recently, Weniger (delta sequence) method has been proposed by the authors of Ref. [1] for resummation of truncated perturbation series in quantum field theories. Those authors presented numerical evidence suggesting that this method works better than Padé 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–Padé 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. PACS number(s): 11.15.Bt, 10.10.Jj, 11.15.Tk, 11.80.Fv, 12.20.-m