 Another tool of constructive QFT is the use of asymptotic series, which can tell us which function the perturbative series is asymptotic to, which perturbative QFT does not. Constructive QFT tries to determine some properties of non-perturbative solutions to the equations of motion which guarantee that certain methods of summing asymptotic expansions will lead to a unique solution (see Hancox-Li 2017, pp. 349–350, for more details). Is the rigorously defined partition function \(Z\) asymptotic to the renormalized perturbative series? Roughly, a function is asymptotic to a series expansion when successive terms of the series provide an increasingly accurate description of how quickly the function grows. The difference between the function and each order of the perturbation series is approximately small. But there are many different functions that have the same asymptotic expansion. Ideally, we want there to be a unique function because then there is a unique non-perturbative solution. The concept of strong asymptoticity requires that the difference between the function and each order of the series is smaller than what was required by asymptoticity. A strongly asymptotic series uniquely determines a function. If there is a strong asymptotic series, then the function can be uniquely reconstructed from the series by Borel summation. The Borel transform of the series is given by dividing the coefficients each term in the series by a factorial of the order of that term and then integrating to recover the exact function. In constructive QFT, the goal is to associate a unique function with a renormalized perturbation series and some kind of Borel summability is the main candidate so far, though the Borel transform cannot remove large-order divergences. The asymptotic behavior of the renormalized perturbation series can be extremely sensitive to the choice of regularization and render it asymptotic to a free field theory even if it appears to describe nontrivial perturbations (see Swanson 2017, p. 11, for more details).