Convergence properties and resummation of the 1/Dexpansion

The semiclassical large-D expansion, with D the number of spatial dimensions, is very effective for some quantum-mechanical problems but not for those with singular potentials. We offer two ways to identify which systems will be poorly approximated by low orders of the 1/D series and show how to repair the difficulty in singular potential problems. The Yukawa potential and $r^2$+${\mathrm{gr}}^4$ anharmonic oscillator are presented as examples. We also discuss the large-order behavior of the 1/D series for the Yukawa problem and argue that this series is divergent.