Resummation of Asymptotic series and non-symptotic scales - Fajardo, Raiseth John T. (Institute of Physics, College of Science, University of the Philippines Diliman, 2015)
This research demonstrates ways of transforming different asymptotic series representing certain functions. This is done by rearranging the asymptotic expansions and rewriting the terms into different forms preferably in terms of transcendental functions. Other than those used in the original series. We employ the moment method of resummation with the use of different kernels and in some example we introduced a scheme we name "superasymptotic integration". The same method is applied to the Poincare Asymptotic Expansion (PAE) of a specific Hankel integral. We apply our resummation scheme on the perturbative contribution of the vacuum-vacuum transition generating functional field theory. The transformed series exhibit asymptotic behavior but instead of having asymptotic sequences as scales, the resulting series are in terms of non-asymptotic scales. The validity of the results and the method per se is checked numerically and the values are comparable to, if not better than, those obtained using the standard PAE. Our "superasymptotic integration" scheme i justified by the sufficiently small relative errors.