Let $X$ be a complex manifold, let $\pi:E\to X$ be a holomorphic vector bundle of rank $m$, and let $p,q\in \mathbb{N}\cup\{0\}$. For every holomorphic frame $e=(e_1,\dots,e_m)$ of $E$ over an [open set](/page/Open%20Set) $U\subset X$, every form $\alpha\in A^{p,q}(U,E)$ has a unique expansion