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Nimz
#2
Mar22-06, 02:07 PM
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:
[tex] \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*} [/tex]

- edit -
well, not quite a complete success, but not a complete failure, either. The original function can be recovered by adding [itex] 0 \cdot \binom{x}{0} + 1 \cdot \binom{x}{1} + 2 \cdot \binom{x}{2} + 0 \cdot \dots = x^2[/itex]. Let's see about the other difference table:

[tex] \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}[/tex]

Much better! So, is anyone interested in how I determined [itex]x^2 3^x + x4^x[/itex] or where my woes with [itex]x^2 2^x + 4^x[/itex] appeared?