  Variational perturbation expansions have recently been used to calculate
directly the strong-coupling expansion coefficients of the anharmonic
oscillator. The convergence is exponentially fast with superimposed
oscillations, as recently observed empirically by the authors. In this note,
the observed behavior is explained and used to determine accurately the
magnitude and phase of the leading Bender-Wu singularity which is responsible
for the finite convergence radius in the complex coupling constant plane.
