the question first asks me to find the taylor expansion of 1/(1-x) by differentiating successively at x=0.
I've done that and obtained the following: 1 + x + x2 + x3 + .......
This is the next part of the question:
b) Use this to find the Taylor expansion for arctan z about z=0 (Hint: recall d/dz (arctan z) = 1/ (1+ z2) and so substitute x= -z2 into the expansion of part a.)
I've substitued x=... into my first expansion but I get: 1 - z2- z4- ........
I know this is not right, because I've done it the long way, but what am I doing wrong?
Thanks in advance.
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Taylor series (doing something wrong!) watch
- Thread Starter
- 16-10-2006 00:30
- 16-10-2006 01:30
Let x = -z^2
and you get 1 - z^2 + z^4-... from part a) which is where youre going wrong by the looks of it.
Then integrate term by term to get
arctan z = z -1/3z^3+ 1/5z^5
- 16-10-2006 23:56