Mellin - Barnes regularization, Borel summation and the Bender - Wu asymptotics for the anharmonic oscillator

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Abstract
. We introduce the numerical technique of Mellin--Barnes integral regularization,which can be used to evaluate both convergent and divergent series. The technique is shownto be numerically equivalent to the corresponding results obtained by Borel summation. Bothtechniques are then applied to the Bender--Wu formula, which represents an asymptotic expansionfor the energy levels of the anharmonic oscillator. We find that this formula is unable to giveaccurate values for the ground-state...

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