Closed-form expression for the SCE-defined function G(s) in zero-dimensional φ^4 theory

Determine whether there exists a closed-form expression, in terms of standard special functions, for the function ℳ(s) defined by the strong-coupling expansion of the zero-dimensional φ^4 two-point correlation function after the change of variables s = 1/√g, where ℳ(s) is the power-series germ obtained from the strong-coupling expansion around s = 0.

Background

In the convergence analysis, the authors introduce the variable s = 1/√g and define a new function ℳ(s) as the germ given by the strong-coupling expansion around s = 0 for the zero-dimensional φ^4 model.

They note that the mapping s = 1/√g is multivalued and that ℳ(s), defined by the series, differs from the analytic continuation of the exact solution around g = ∞. While numerical evidence suggests a disk of analyticity for ℳ(s), the authors explicitly state that they have not found a closed-form expression and that such an expression might exist.