  Using quantum differential operators, we construct a super representation of
$U_v(\mathfrak{gl}_{m|n})$ on a certain polynomial superalgebra. We then extend
the representation to its formal power series algebra which contains a
$U_v(\mathfrak{gl}_{m|n})$-submodule isomorphic to the regular representation
of $U_v(\mathfrak{gl}_{m|n})$. In this way, we obtain a presentation of
$U_v(\mathfrak{gl}_{m|n})$ by a basis together with explicit multiplication
formulas of the basis elements by generators.
