  The multi-point Taylor polynomial, which is the general, unique and of
minimum degree ($mk+m-1$) polynomial $P_{k,m}(x)$ which interpolates a
function's derivatives in multiple points is presented in its explicit form. A
proof that this expression satisfies the multi-point Taylor polynomial's
defining property is given. Namely, it is proven that for a k-differentiable
function $f$ and a set of different m-points $\{a_1,...,a_m\}$, this polynomial
satisfies $P^{(n)}_{k,m}(a_i) = f^{(n)}(a_i)\quad \forall \, i = 1,...,m\quad
\&\quad \forall \, n = 0,...,k$. A discussion regarding previous expressions
presented in the literature, which mostly consisted in recursion formulas and
not explicit formulas, is made.
