Extracting accurate numerical approximations from divergent integrals via "superasymptotic" integration

Abstract

We do resummation on the exponential integral function via N-level Borel summation. The resulting integrals are however divergent. Nevertheless, good approximation can still be extracted from these divergent integrals by truncating the integration limit up to some cut-off point. Our method of “superasymptotic integration” is justified by the small relative error obtained by the resummation.