Completions of quantum coordinate rings

Given an iterated skew polynomial ring $C[y_1;\tau_1,\delta_1]\ldots [y_n;\tau_n,\delta_n]$ over a complete local ring $C$ with maximal ideal $\mathfrak{m}$, we prove, under suitable assumptions, that the completion at the ideal $\mathfrak{m} + \left\langle y_1,y_2,\ldots,y_n\right\rangle$ is an iterated skew power series ring. Under further conditions, the completion becomes a local, noetherian, Auslander regular domain. Applicable examples include quantum matrices, quantum symplectic spaces, and quantum Euclidean spaces.