  The leading correction from interactions to the transition temperature T_c
for Bose-Einstein condensation can be obtained from a nonperturbative
calculation in the critical O(N) scalar field theory in 3 dimensions with N=2.
We show that the linear delta expansion can be applied to this problem in such
a way that in the large-N limit it converges to the exact analytic result. If
the principal of minimal sensitivity is used to optimize the convergence rate,
the errors seem to decrease exponentially with the order in the delta
expansion. For N=2, we calculate the shift in T_c to fourth order in delta. The
results are consistent with slow convergence to the results of recent lattice
Monte Carlo calculations.
