How would I go about showing that the third coefficient of the 2nd order Newton's interpolating polynomial is :
$a3=D^2y1= \frac{Dy2-Dy1}{x3-x1}= \frac{\frac{y_3-y_2}{x_3-x_2}-\frac{y_2-y_1}{x_2-x_1}}{x_3-x_1}$
I dont know how to use math equations here, but I hope putting this in word and pressing the INSERT EQUATION you can see what I'm trying to prove ...
Whenever I try doing it the normal way (placing $x=x_0$, $x=x_1$, $x=x_2$ etc..), I get : $\frac{\frac{y_3-y_1}{x_3-x_1}-\frac{y_2-y_1}{x_2-x_1}}{x_3-x_2}$
So how can I prove that both of these equations are the same !!?