How to write a second order Taylor polynomial for $f:\mathbb R^n\to \mathbb R^n$.

Question

If $f:\mathbb R^n\to \mathbb R$, is $\mathcal C^2$, then we can write \begin{align*} f(x+h)&=f(x)+\left<\nabla f(x),h\right>+h^TH_f(x)h+o(|h|^2)\\ &= f(x)+\left<\nabla f(x),h\right>+\left<h, H_f(x)h\right>+o(|h|^2) \end{align*} where $H_f(x)$ is the Hessian matrix. If now, for example $f:\mathbb R^n\to \mathbb R^n$, how can I write the previous expression ? If $J_x(f)$ is the Jacobian, then $$f(x+h)=f(x)+J_f(x)h+o(h),$$ but since the Hessian is a sort of matrix $n\times n\times n$ (called a tensor). But is there a nice way to write the term of second order ?