Equation 21.12.26E34E6BC222DC

\begin{equation} \begin{split} \left( \frac{\mathrm{i}}{2\pi }\right)^ n\int _{\mathbb {C}^{*n}}f(a_1,\ldots ,a_ n) \left(\sum _{i,j=1}^ n \partial _{i,j}F(a_1,\ldots ,a_ n)z_ i^{-1}\overline{z_ j}^{-1}\mathrm{d}z_ i\wedge \mathrm{d}\overline{z_ j}\right)^ n=\\ n!\int _{\mathbb {R}^ n} f \det \nabla ^2 F\, \mathrm{d}\operatorname{vol}. \end{split} \end{equation}