D-dimensional Ideal Quantum Gases in $A{r}^n+B{r}^{-n}$ Potential

The paper is concerned with thermostatistics of both $D$-dimensional Bose and Fermi ideal gases in a confining potential of type $A{r}^n+B{r}^{-n}$. The investigation is performed in the framework of the semiclassical approximation. Some physical quantities for such systems are derived, like density of states, density profiles and number of particles. Bose-Einstein condensation (BEC) is discussed in the high and low temperature regimes.