Find the radius of convergence of the power series expansion of the function $$f(z) = \frac{e^{z^2}}{z(z − 1)(z − 2)^2}$$ at $z_{0} = i + 1$
The question asks me to find the radius of convergence without getting power series expansion.
My approach:
Since I know that from Cauchy integral theorem, f(z) = $a_{n}(z-z_{0})^n$ where $a_{n} = f^{n}(z_{0})/n!$ and I also tried to use the fact that $e^{z^2}$ power series expansion, but it looks like this was not allowed. Also since I know $z_{0}$, does this mean i + 1 is the radius of convergence?