  For lambda phi^4 models, the introduction of a large field cutoff improves
significantly the accuracy that can be reached with perturbative series but the
calculation of the modified coefficients remains a challenging problem. We show
that this problem can be solved numerically, and analytically in the limits of
large and small field cutoffs, for the ground state energy of the anharmonic
oscillator. For the two lowest orders in lambda, the approximate formulas
obtained in the large field cutoff limit extend unexpectedly far in the low
field cutoff region and there is a significant overlap with the small field
cutoff approximation. For the higher orders, this is not the case, however the
shape of the transition between the small field cutoff regime and the large
field cutoff regime is approximately order independent.
