discrete calculus - Am I correctly computing $\Delta(x^\overline m)$?

Notation definitions according to Concrete Mathematics:$\Delta f(x) = f(x+1) - f(x)$$x^\underline m = x(x-1)...(x-m+1)$, integer $m \ge 0$ (Read aloud as "x to the m falling.")$x^\overline m = x(x+1)...(x+m-1)$, integer $m \ge 0$ (Read aloud as "x to the m rising.")I derived $\Delta f(x^\underline m)$ for myself, and it is also given in the book, as: $mx^\underline{m-1}$ (A fun result to calculate!)I then tried to compute $\Delta(x^\overline m)$, which is not shown in the book, and got the slightly more unwieldy result:$m(x+1)^\overline{m-1}$...Read more