MELLIN-BARNES REGULARIZATION, BOREL SUMMATION AND THE BENDER-WU ASYMPTOTICS FOR THE ANHARMONIC-OSCILLATOR

We introduce the numerical technique of Mellin-Barnes integral regular ization, which can be used to evaluate both convergent and divergent s eries. The technique is shown to be numerically equivalent to the corr esponding results obtained by Borel summation. Both techniques are the n applied to the Bender-Wu formula, which represents an asymptotic exp ansion for the energy levels of the anharmonic oscillator We find that this formula is unable to give accurate values for the ground-state e nergy, particularly when the coupling is greater than 0.1. As a conseq uence, the inability of the Bender-Wu formula to yield exact values fo r the energy level of the anharmonic oscillator cannot be attributed t o its asymptotic nature.