Finite polynomial derivative interpolation at an arbitrary point

Over a field $K$ of characteristic zero, any finite list of derivative values can be prescribed at a point $\xi\in K$. For any sequence $a_k\in K$ and integer $N\ge0$, there is a polynomial $P$ such that $P^{(k)}(\xi)=a_k$ for all $k<N$. A witness is the finite Taylor polynomial $\sum_{k<N}a_k(X-\xi)^k/k!$. This supplies the polynomial interpolation ingredient used to choose the derivative rows in the ordinary cyclic-vector construction. It does not itself construct the covariant derivative rows or prove scalar-equation minimality.