Divided difference
= Divided difference
{wiki}
For distinct nodes,
$$
f[x_0,\ldots,x_k]
=\sum_{j=0}^k\frac{f(x_j)}
{\prod_{i\ne j}(x_j-x_i)}.
$$
It is the leading coefficient of the interpolating polynomial through those nodes and obeys
$$
f[x_0,\ldots,x_k]
=\frac{f[x_1,\ldots,x_k]-f[x_0,\ldots,x_{k-1}]}
{x_k-x_0}.
$$