Moment-Borel-Laplace Method and Summability

In this chapter, we are concerned with a generalization of the Borel-Laplace method in terms of the general moment-Borel and moment-Laplace operators. The resulting characterization of the k-summability (see Sect. 9.1) will thus provide an alternative tool to study the k-summability of the formal power series solutions of certain partial differential equations. Some applications are presented in Sect. 9.2.