Thread: Difference tables View Single Post
 P: 81 Let's see. I looked at the first 400 or so posts on the LaTex tutorial page. Maybe I can make this look prettier. Here's the first difference table, hopefully formatted how I wanted it: $$\begin{gather*} 0 \, 1 \, 4 \, 9 \, 16 \, 25\, \dots \\ 1 \, 3 \, 5 \, 7 \, 9 \, \dots \\ 2 \, 2 \, 2 \, 2 \, \dots \\ 0 \, 0 \, 0 \, \dots \end{gather*}$$ - edit - well, not quite a complete success, but not a complete failure, either. The original function can be recovered by adding $0 \cdot \binom{x}{0} + 1 \cdot \binom{x}{1} + 2 \cdot \binom{x}{2} + 0 \cdot \dots = x^2$. Let's see about the other difference table: $$\begin{array}{c c c c c c c c c c c c} 1 && 3 && 9 && 27 && 81 && 243 & \dots \\ & 2 && 6 && 18 && 54 && 162 & \dots \\ & & 4 && 12 && 36 && 108 & \dots \\ & & & 8 && 24 && 72 & \dots \\ & & & & 16 && 48 & \dots \\ & & & & & 32 & \dots \end{array}$$ Much better! So, is anyone interested in how I determined $x^2 3^x + x4^x$ or where my woes with $x^2 2^x + 4^x$ appeared?