 $$ \frac{0}{\sqrt{m!n!}} \left. \left[ \frac{\partial^{n+m} \left( \langle \alpha | \hat{F} | \alpha \rangle e^{\alpha^*\alpha} \right)}{\partial\alpha^{*m}\partial\alpha^n }\right] \right|_{\alpha^*=0 \\ {\alpha=0}} = \frac{0}{\sqrt{m!n!}} \left. \left[ \frac{\partial^{n+m}