Resummation of the Poincaré asymptotic expansion of the Hankel integral by Borel summation and superasymptotic integration

  • Nathalie Liezel Rojas National Institute of Physics, University of the Philippines Diliman
  • Eric Galapon National Institute of Physics, University of the Philippines Diliman

Abstract

We subject the Poincaré asymptotic expansion of the Hankel integral to resummation through Borel transformation to determine an asymptotic expansion that can approximate the Hankel integral for small values of the asymptotic parameter. Two cases are considered where the odd and even values of the series are separated. In the resummation process, the integral after Borel summation happens to be divergent thus we perform superasymptotic integration. We find that both resummations show superiority than its Poincaré asymptotic expansion in approximating the value of the Hankel integral for small values of the parameter.

Published
2019-05-22
How to Cite
[1]
N. L. Rojas and E. Galapon. Resummation of the Poincaré asymptotic expansion of the Hankel integral by Borel summation and superasymptotic integration, Proceedings of the Samahang Pisika ng Pilipinas 37, SPP-2019-2D-03 (2019). URL: https://paperview.spp-online.org/proceedings/article/view/SPP-2019-2D-03.
Section
Theoretical and Mathematical Physics