Finding the radius of convergence of a series.

[FLms]

Homework Statement

What is the radius of convergence of the Taylor Series of the function f(z) = z cot(z), at the point z = 0?

Homework Equations

Taylor series is given by:
\sum_{k=0}^{\infty} \frac{f^{(k)}(z_{0})}{k!} (z - z_{0})

And the radius R by:
\lim_{n \to \infty} |\frac{a_{n}}{a_{n+1}}|

The Attempt at a Solution

The problem here is to find a pattern to represent the function as a series.
I did some derivatives and tried to substitute cot(z) for it's representation as an exponential, but all I've got is division by zero.

f(z) = z cot(z) = z (\frac{e^{2z} + 1}{e^{2z} -1})

\frac{d f}{dz} = \frac{-e^{4z} + 1 + 4 z e^{2*z}}{(e^{2z}-1)^2}
And so on...
At the point z = 0, the function blows up.

As a trigonometrical representation, it's the same thing.
\frac{df(z)}{dz} = cot(z) - z csc(z)


I'm not really going anywhere here.
Please help.

 

[dikmikkel]

Maybe the convergence radius is zero ?