Now that CaptainBlack and Jhevon have helped me out with Latex notation I can ask my question.
I was working on taylor polynomials and I ran into a little snag which has me stumped.
For the function
we get the taylor series:
So for
we get
Yet if we construct the taylor polynomial for
from scratch:
for x= 0
in fact we dont see a non zero constant term until the 12th order differential:
Which looks quite crazy I've just realised. Some of the terms are
.
So if we get this, then the numerator on the second term of the taylor polynomial should be massive. So why does letting
work? I understand the logic behind it I suppose, as the taylor polynomial work for any value of
and
is just a finite number (for any finite
and for this
function, I know it doesn't hold for all functions). But why does the method of constructing the taylor polynomial from the formula:
fail?