Time to make something more complicated

x²... Very innocent looking thing. But let's say you want to jazz it up a little. Make it more, I don't know, long?? Here's what I think: x² is too short.

First, we need a function:

Next, here's a table of values (ignore g(x) for now):

x	f(x)	g(x)
1	1	3
2	4	5
3	9	7
4	16	9
5	25	11
6	36	13
7	49	15
8	64	17
9	81	19
10	100	21

As you can see, the pattern emerges sooner or later. Values of g(x) represents the difference between f(x+1)-f(x)

From the table, we can conclude that

This keeps going on until
Now, writing that out is incredibly messy, so, I'm gonna use the Greek letter, sigma!! It's the very-cool-looking letter that looks like an E. So, summing it up, you'll get:

But,Therefore,

And because,

Then,Some more,

So, it is possible to write it out as:
And with that, we have finally made x² a little bit more complicated. Hahaha! Have a nice day!