  The analytic properties of the ground state resonance energy E(g) of the
cubic potential are investigated as a function of the complex coupling
parameter g. We explicitly show that it is possible to analytically continue
E(g) by means of a resummed strong coupling expansion, to the second sheet of
the Riemann surface, and we observe a merging of resonance and antiresonance
eigenvalues at a critical point along the line arg(g) = 5 pi/4. In addition, we
investigate the convergence of the resummed weak-coupling expansion in the
strong coupling regime, by means of various modifications of order-dependent
mappings (ODM), that take special properties of the cubic potential into
account. The various ODM are adapted to different regimes of the coupling
constant. We also determine a large number of terms of the strong coupling
expansion by resumming the weak-coupling expansion using the ODM, demonstrating
the interpolation between the two regimes made possible by this summation
method.
