Newton forward interpolation
= Newton forward interpolation
{c}
For equally spaced nodes $x_0,x_0+h,\ldots,x_0+dh$, write $t=(x-x_0)/h$. The interpolating <polynomial> is $P(x)=\sum_{j=0}^d\binom tj\Delta_h^j f(x_0)$. A table of <forward differences> supplies its coefficients; for a <polynomial> of degree at most $d$, the formula reproduces the function exactly.