Resummation on the Poincare asymptotic expansion of the Hankel Integral via Borel summation

Abstract

We resum the Poincare asymptotic expansion (PAE) of the Hankel integral function by means of Borel summation. We also do a hyperasympotic approximation on the original asymptotic expansion and compare the relative error associated with the reexpansions. The resummed series is proved to be numerically more accurate than the PAE but is inferior to the hyperasymptotic approximation. The resulting series incorporates scale that does not fall under the known technical definition of asymptotic scales and is written in terms of non-asymptotic scale.