# Thread: Complex Taylor Series

1. ## Complex Taylor Series

I'm having troubles with this one problem.

Derive the Taylor Series of $f(z)$ centered around $z_{0} = 0$ by multiplying the top and bottom by $1-z$ where $f(z) = \frac{1}{1+z+z^2}$

2. Originally Posted by Haven
I'm having troubles with this one problem.

Derive the Taylor Series of $f(z)$ centered around $z_{0} = 0$ by multiplying the top and bottom by $1-z$ where $f(z) = \frac{1}{1+z+z^2}$
Using the hint, we have:

$f(z)=\frac{1-z}{1-z}\cdot\frac{1}{1+z+z^2}=(1-z)\left[\frac{1}{1-z^3}\right]=(1-z)\left[1+z^3+\frac{z^6}{2}+\frac{z^9}{6}+\frac{z^{12}}{24 }+...\right]$

3. Oh my gosh, it's so obvious now. I was trying to do partial fractions or something stupid like that. Thanks alot, and nice joke in your signature

4. You're welcome and thanks. I assume you were referring to the Hilbert quote I had (seeing as I changed my signature literally five minutes ago).

5. Originally Posted by Haven
Oh my gosh, it's so obvious now. I was trying to do partial fractions or something stupid like that. Thanks alot, and nice joke in your signature
You will find that there is a "thanks" button on the right at the bottom of the helpful post for you if you wish to thank the helpful poster.

CB