Question 8.5: Simplify Eq. (8.2.32) for evenly spaced data.

With x_2 = x_0 + 2h and x_1 = x_0 + h, we have

f[x_2, x_1, x_0] =\left[\frac{f(x_2)-f(x_1)}{h}-\frac{f(x_1)-f(x_0)}{h} \right] \frac{1}{2h}           (8.2.51)

which reduces to

f[x_2, x_1, x_0]=\frac{f(x_2)-2f(x_1)+f(x_0)}{2h^2}                   (8.2.52)

Does this look familiar? We will return to this question shortly.