follows $$\begin{aligned}
{\rm F}\star {\rm G} &=& \mu_\star \{ {\rm F}\otimes {\rm G} \} \nonumber\\
&=& \mu \{ {\cal F}^{-1}\, {\rm F}\otimes {\rm G}\} \nonumber\\
&=& \mu \{ e^{-\frac{1}{2}C^{\alpha\beta}\p_\alpha \otimes\p_\beta
-
\frac{1}{2}\bar{C}_{\dot{\alpha}\dot{\beta}}\bar{\p}^{\dot{\alpha}}
\otimes\bar{\p}^{\dot{\beta}}} {\rm F}\otimes {\rm G} \} \nonumber\\
&=& {\rm F}\cdot {\rm G} - \frac{1}{2}(-1)^{|{\rm F}|}C^{\alpha\beta}
(\p_\alpha {\rm F})\cdot(\p_\beta {\rm G}) -
\frac{1}{2}(-1)^{|{\rm F}|}\bar{C}_{\dot{\alpha}\dot{\beta}}
(\bar{\p}^{\dot{\alpha}} {\rm F})
(\bar{\p}^{\dot{\beta}} {\rm G})\nonumber\\
&&- \frac{1}{8}C^{\alpha\beta}C^{\gamma\delta}(\p_\alpha\p_\gamma {\rm F})
\cdot(\p_\beta\p_\delta {\rm G})
- \frac{1}{8}\bar{C}_{\dot{\alpha}\dot{\beta}}\bar{C}_{\dot{\gamma}\dot{\delta}}
(\bar{\p}^{\dot{\alpha}}\bar{\p}^{\dot{\gamma}} {\rm F})
(\bar{\p}^{\dot{\beta}}\bar{\p}^{\dot{\delta}} {\rm G}) \nonumber\\
&&- \frac{1}{4}C^{\alpha\beta}\bar{C}_{\dot{\alpha}\dot{\beta}}
(\p_\alpha\bar{\p}^{\dot{\alpha}}{\rm F})
(\p_\beta\bar{\p}^{\dot{\beta}} {\rm G}) \nonumber\\
&& + \frac{1}{16}(-1)^{|{\rm F}|}
C^{\alpha\beta}C^{\gamma\delta}\bar{C}_{\dot{\alpha}\dot{\beta}}
(\p_\alpha\p_\gamma\bar{\p}^{\dot{\alpha}} {\rm F})
(\p_\beta\p_\delta\bar{\p}^{\dot{\beta}} {\rm G}) \nonumber\\
&& + \frac{1}{16}(-1)^{|{\rm F}|}C^{\alpha\beta}\bar{C}_{\dot{\alpha}
\dot{\beta}} \bar{C}_{\dot{\gamma}\dot{\delta}}
(\p_\alpha\bar{\p}^{\dot{\alpha}}\bar{\p}^{\dot{\gamma}} {\rm F})
(\p_\beta\bar{\p}^{\dot{\beta}}\bar{\p}^{\dot{\delta}} {\rm G})
\nonumber\\
&& + \frac{1}{64}C^{\alpha\beta}C^{\gamma\delta}
\bar{C}_{\dot{\alpha}\dot{\beta}}\bar{C}_{\dot{\gamma}\dot{\delta}}
(\p_\alpha\p_\gamma\bar{\p}^{\dot{\alpha}}\bar{\p}^{\dot{\gamma}}
{\rm F})(\p_\beta\p_\delta \bar{\p}^{\dot{\beta}}\bar{\p}^{\dot{\delta}}
{\rm G}), \label{star}\end{aligned}$$ where $|{\rm F}| = 1$ if ${\rm F}$ is odd (fermionic) and $|{\rm F}|=0$ if ${\rm F}$ is even (bosonic) and the pointwise multiplication $\mu$ is the bilinear map from the tensor product to the space of superfields (functions). The definition of the multiplication $\mu_\star$ is given in the second line. No higher powers of $C^{\alpha\beta}$ and $\bar{C}_{\dot{\alpha}\dot{\beta}}$ appear since the derivatives $\p_\alpha$ and $\bar{\p}^{\dot{\alpha}}$ are Grassmanian. Expansion of the $\star$-product (\[star\]) ends after the fourth order in the 