I encountered the following power series, and while I know a couple of ways to determine radius of convergence, I wasn't able to figure out how to evaluate the appropriate limit to get said radius. Can anyone help?
What is the radius of convergence of the power series $\sum_{n=0}^\infty\cos\left(\alpha\sqrt{1+n^2}\right)z^n,$ where $\alpha$ is any real number? What if $\alpha$ is a complex number?