  The quartic confining potential has emerged as a key ingredient to obtain
fast rotating vortices in BEC as well as observation of quantum phase
transitions in optical lattices. We calculate the critical temperature $T_c$ of
bosons at which normal to BEC transition occurs for the quartic confining
potential. Further more, we evaluate the effect of finite particle number on
$T_c$ and find that $\Delta T_c/T_c$ is larger in quartic potential as compared
to quadratic potential for number of particles $ < 10^5$. Interestingly, the
situation is reversed if the number of particles is $\gtrsim10^5$.
