  In this work, we investigate a coordinate space structure function ${\cal
E}(z^2m^2,\lambda)$ in the 2D $U(N)$ Gross-Neveu model to the next-to-leading
order in the large-$N$ expansion. We analytically perform the twist expansion
in the Bjorken limit through double Mellin representations. Hard and
non-perturbative scaling functions are naturally generated in their Borel
representations with detailed enumerations and explicit expressions provided to
all powers. The renormalon cancellation at $t=n$ between the hard functions at
powers $p$ and the non-perturbative functions at powers $p+n$ are explicitly
verified, and the issue of ``scale-dependency'' of the perturbative and
non-perturbative functions is explained naturally. Simple expressions for the
leading power non-perturbative functions are also provided both in the
coordinate space and the momentum-fraction space ($0<\alpha<1$) with
``zero-mode-type'' subtractions at $\alpha=0$ discussed in detail. In addition
to the Bjorken limit, we also perform the threshold expansion of the structure
function up to the next-to-next-to-leading threshold power exactly and
investigate the resurgence relation between threshold and ``Regge''
asymptotics. We also prove that the twist expansion is absolutely convergent
for any $0<z^2<\infty$ and any $ \lambda \in iR_{\ge 0}$.
