Large-order shifted<i>1/N</i>expansions

Abstract

The hypervirial perturbative method is used to obtain large-order shifted 1/N expansions, where N is the number of spatial dimensions. Numerical investigation shows that the usually chosen shift is useful only when low-order expansions are considered. An appropriate order-dependent shift proves to lead to highly accurate large-order expansions. The class of power-law potentials is discussed as an illustrative example.