Let (R,m,k) be a regular local k-algebra satisfying the weak Jacobian criterion, and such that k_R/k is an algebraic field extension. Let D be the ring of k-linear differential operators of R. We give an explicit decomposition of the DR-module D/Dm^(n+1) as a direct sum of simple modules, all isomorphic to D/Dm, where certain “Pochhammer” differential operators are used to describe generators of the simple components.