Where is this function defined and analytic?
Our function is analytic wherever it has a convergent power series. Since (I am assuming) $\sin(z)$ and $\cos(z)$ are analytic the quotient is analytic wherever $\cos(z) \not\to 0$???
Is there more detail to this that I am missing? Without Cauchy is there a way to determine analyticity etc...
Further more, once we have found the first few terms as I have
How do we make an estimate of the radius of convergence? Do I make an observation that the terms are getting close to $0$ and say perhaps the $nth$ root is heading there as well, $\therefore$ $R=\infty$. I'm fairly lost on this part.
Thanks for your help!