Complex Taylor Series

**Haven** · November 14th 2009, 07:45 PM

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 $f(z) = \frac{1}{1+z+z^2}$

**redsoxfan325** · November 14th 2009, 10:38 PM

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:

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

**Haven** · November 14th 2009, 11:43 PM

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

**redsoxfan325** · November 14th 2009, 11:45 PM

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).

**CaptainBlack** · November 15th 2009, 12:23 AM

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

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