Extracting Non-Perturbative Data from the Parametrized Hypergeometric approximants of a given divergent series

The strong-coupling asymptotic behavior is not known till now for even a simple quantum field theory like the Φ⁴ scalar field model. In our previous work (e.g. Physical Review D 101 (10), 105006, The European Physical Journal C 81 (1), 1-13 ) we introduced and applied the hypergeometric-Meijer resummation algorithm. Other than its accurate prediction for physical quantities represented by divergent series, we stress here its accurate predictions for the asymptotic behavior of the given series. We show that one can get accurate predictions for the strong-coupling data as well as the large-order asymptotic data for parametrizing the approximants using only perturbative data as input.