Does a multivariate expansion of the Newton series exist? If so what is its formulae?
In the scalar case we have that by expansing around $0$ if $x \in Z$ then:
\begin{equation} f(x) = \sum_{m=0}^{\infty}\frac{1}{m!} \Delta_1^m f(x)|_{x=0}(x)_m \end{equation}
where $\Delta_1^m$ is the forward finite difference appleid $m$ times one step ahead and $(x)_m$ is defined as follows $(x)_m = \prod_{n=0}^{m-1}(x-n)$, i.e. the falling factorial
Does a multivariate form exist, analagously to the Taylor Expansion? Say for instance to expand $f(x,y)$?
