  We compare and contrast three different perturbative expansions for the
quartic anharmonic oscillator wavefunction and apply a modified Borel summation
technique to determine the energy eigenvalues. In the first two expansions this
provides the energy eigenvalues directly however in the third method we tune
the wavefunctions to achieve the correct large x behaviour. This tuning
technique allows us to determine the energy eigenvalues up to an arbitrary
level of accuracy with remarkable efficiency. We give numerical evidence to
explain this behaviour. We also refine the modified Borel summation technique
to improve its accuracy. The main sources of error are investigated with
reasonable error corrections calculated.
