I have the following question, and I don't even know where to begin:
Do functions $f$ or $g$ exist which are analytic at the point $z=0$ and satisfy the conditions: $f(\frac{1}{n})=f(\frac{-1}{n})=\frac{1}{n^2}$, and $g(\frac{1}{n})=g(\frac{-1}{n})=\frac{1}{n^3}$?