Second Characterization of the k-Summability: The Borel-Laplace Method

The method of summation of a formal power series \(\widetilde {f}(t)\in \mathbb C[[t]]\) by means of Borel and Laplace operators was first introduced by E. Borel in the “simplest case” of level 1, then generalized to any level \(k>0\) .