Initial results of a research collaboration between SCL's path integral group and Dr. Axel Pelster will be presented as a poster during the poster session of the Dynamics and Statistical Physics Division at the 2008 Spring Conference of the German Physical Society. The presented results focus on a recently derived set of recursive relations for improved effective path integral actions. Higher level effective actions are used for N=1 approximation to path integrals (one time slice), when there is no integrals, and path integrals are given in terms of closed algebraic expressions. This approximation is successfully used for the calculation of the critical temperature of the Bose-Einstein condensate of Rb atoms in an anharmonic trap.