  Through Borel summation, one can often reconstruct an analytic solution of a
problem from its asymptotic expansion. We view the effectiveness of Borel
summation as a regularity property of the solution, and we show that the
solutions of certain differential equation and integration problems are regular
in this sense. By taking a geometric perspective on the Laplace and Borel
transforms, we also clarify why "Borel regular" solutions are associated with
special points on the Borel plane. The particular classes of problems we look
at are level 1 ODEs and exponential period integrals over one dimensional
Lefschetz thimbles. To expand the variety of examples available in the
literature, we treat various examples of these problems in detail.
