Bose-Einstein condensation temperature for an anisotropic effective mass ($k_B{T}_c=2\pi {\hslash }^2[n/(\sqrt{\gamma }\zeta (3/2)){]}^{2/3}/m$)

For a one-component ideal Bose gas with masses $(m,m,\gamma m)$, insert the anisotropic ideal-gas density of states in the excited-state number integral at chemical potential zero. The substitution $x=\epsilon /(k_{B}T)$ gives $n=\sqrt{\gamma }(m{k}_{B}T/(2\pi {\hslash }^2){)}^{3/2}\zeta (3/2)$, which yields the displayed transition temperature. Thus at fixed density and the two lighter masses, $T_c\propto {\gamma }^{-1/3}$. This continuum ideal-gas result does not supply a finite-temperature transition for decoupled two-dimensional layers.