The effective potential V is considered in massless λϕ^4_4 theory. The expansion of V in powers of the coupling λ and of the logarithm of the background field ϕ is reorganized in two ways; first as a series in λ alone, then as a series in ϕ alone. By applying the renormalization group (RG) equation to V, these expansions can be summed. Using the condition V^'(v) = 0 (where v is the vacuum expectation value of ϕ) in conjunction with the expansion of V in powers of ϕ fixes V provided v≠ 0. In

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... case, the dependence of V on ϕ drops out and V is not analytic in λ. Massless scalar electrodynamics is considered using the same approach.