There is this question I saw somewhere, saying:
Assume $f = \sin(2x) $, what's the value of divided differences $ f[0, 0, 0] $ and $ f[\frac{\pi}{2}, \frac{\pi}{2}, \frac{\pi}{2}, \frac{\pi}{2}] $?
So, I know the final answer is $ 0 $ and $\frac{4}{3}$, but I can't understand why. Because it seems to me that by applying the definition of divided difference, there's gonna be some $0$'s in the denominator (because well, all the $x$'s in the definition are the same) and thus the divided difference should be undefined.