  Allowing a single electron to hop to next-nearest neighbours (NNN) in
addition to the closest atomic sites in the Holstein model, a modified Trugman
method is applied to exactly calculate the effect on the polaronic effective
mass in one, two, and three dimensions, building on the previous study of the
one-dimensional NNN Holstein model. We also present perturbative calculations
and a heuristic scaling factor for the coupling strength and ion frequency to
nearly map the NNN Holstein model back onto the original Holstein model. When
account is taken of the modified electronic bandwidth near the electron energy,
we find that including NNN hopping effectively increases the polaron effective
mass.
