Abstract
The linear delta expansion is applied to the three-dimensional O(N) scalar field theory at its critical point in a way that is compatible with the large-N limit. For a range of the arbitrary mass parameter, the linear delta expansion for <phi-->(2)> converges, with errors decreasing as a power of the order n in delta. If the principal of minimal sensitivity is used to optimize the convergence rate, the errors seem to decrease exponentially with n.
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