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We prove a structure theorem for differential operators in the 0-th term of the V-filtration relative to a free divisor. manifold. As an application, we give a formula for the logarithmic de Rham complex with respect to a free divisor in terms of V 0 -modules, which generalizes the classical formula for the usual de Rham complex in terms of D-modules, and the formula of Esnault-Viehweg in...