In the previous note that I've written I said
This can come in handy today!
We know the function image of is:
First we can say because when or or the and . But let we see the function image (the blue line):
This fits too badly! and when then . Can we let when ?
Let which is a constant. So
when . After expansion, derivation, only "" is left, and the others are all 0 because they contain x (ie 0). So
Then it will become like this:
It's great! The same,
only "" is left, and the others are all 0 because they contain x (ie 0). So
And so on:
We also know . Then
and also is
Therefore, the split items with items on the left and right are equal.
In the left of the formula, it has and in the right of the formula -- how many does it have?
We must have , remove the first , it takes a to form . So we have: