An analytical solution for the critical number of particles for stable bose-einstein condensation under the influence of an anisotropic potential

we have considered a bose gas in an anisotropic potential. applying the the gross-pitaevskii equation (gpe) for a confined dilute atomic gas, we have used the methods of optimized perturbation theory and self-similar root approximants, to obtain an analytical formula for the critical number of particles as a function of the anisotropy parameter for the potential. the spectrum of the gpe is also discussed.