  It is well known that perturbative expansions of path integrals are
divergent. These expansions are to be understood as asymptotic expansions,
which encode the limiting behaviour of the path integral for positive small
coupling. Conventionally, the method of Borel summation assigns a finite answer
to the divergent expansion. Still, the Borel sum might not encode the full
information of a function, because it misses exponentially small corrections.
In the present work, we consider a slight variation of the conventional Borel
summation, in which a generalised Borel transform (an inverse Laplace
transform) is followed by a directional Laplace transform. These new tools will
allow us to give perhaps better answers to typical problems in Borel summation:
missing exponential corrections and ambiguities in the Borel summation. In
addition, we will define resurgence as a connection between the discontinuity
of a function and the coefficients of its asymptotic expansion. From this
definition, we will be able to reduce resurgence to the problem of missing
exponential corrections in asymptotic expansions and understand, within a
unified framework, different approaches to resurgence found in the literature.
