Analytic continuation of residue currents

Let $X$ be a complex manifold and $f\text{\hspace{0.17em}⁣}:X\to {\text{C}}^p$ a holomorphic mapping defining a complete intersection. We prove that the iterated Mellin transform of the residue integral associated to $f$ has an analytic continuation to a neighborhood of the origin in ${\text{C}}^p$.