I'm tasked with finding the analytic continuation of $f(z)$ to the entire z-plane. Also, are there any points where the continuation in not analytic?
Analytic continuation is new to me so I'm unsure what how to approach the problem. My instinct is to use the real axis, where $f(z)=f(x)$, to relate the above series to a known real series where I know the explicit expression for $f(x)$. Would this be a valid approach, or should I proceed by different means?