what's the concrete formula of the second-order taylor expansions for real-valued functions with complex variables?

Question

I read a paper where the second-order taylor expansions for real-valued functions with complex variables is given as follows: $f(x)=f(x_{0})+\Re\{\triangledown^{H}f(x_{0})\cdot(x-x_{0})\}+\frac{1}{2}(x-x_{0})^{H}\cdot H(x_{0})\cdot(x-x_{0})$, where $x\in \mathbb{C}^{n\times1}$ and $f(x)$ is real. I find the expression for $\triangledown f(x_{0})$ in Matrix CodeBook which is given as: $\triangledown f(x)=2\cdot\frac{\partial f(x)}{\partial x^{*}}$, but couldn't find the concrete expression for the Hessian matrix $H(x_{0})$. So what's the concrete expression for the Hessian matrix $H(x_{0})$?