For given equidistant values $u_{-1}, u_{0}, u_{1},$ and $u_{2}$, a value is interpolated by Lagrange's formula. Show that it may be written in the form
$$u_{x} = yu_{0} + xu_{1} + \frac{y\left (y^{2} -1 \right )}{3!}\Delta ^{2}u_{-1} + \frac{x\left (x^{2} -1 \right )}{3!}\Delta ^{2}u_{0},$$ where $x+y=1$
The point where I am facing a doubt is:
a) Are the $x's$ equidistant (i.e. $-1, 0, 1, 2$) or the $y's$ equidistant or both (which seems improbable).
b) Even in either cases, I am not able to proceed.