  Let $f_1$, $f_2$, and $f_3$ be holomorphic functions on a complex manifold
and assume that the common zero set of the $f_j$ has maximal codimension, i.e.,
that it is a complete intersection. We prove that the iterated Mellin transform
of the residue integral has an analytic continuation to a neighborhood of the
origin in $\mathbb{C}^3$. We prove also that the natural regularization of the
residue current converges unrestrictedly.
