Is there any holomorphic function in a unit ball Is there any holomorphic function in a unit ball such that $f(1/n)=n^{-5/2}$ for $n=2,3,\dots$
Natural candidate is $f(z)=z^{5/2}$ But it isn't holomorphic obviously inside that ball. Can you tell me whatI should check?

If $f$ is such a function, then $g(z)=f(z)^2$ conincides with $z\mapsto z^5$ on a sequence of points converging to $0$. Hence $g(z)=z^5$ for all $z$. If we write $f(z)=z^kh(z)$ with $k\in\mathbb N_0$, $h$ holomorphic, $h(0)\ne0$, we find that $z^{2k}h(z)^2=z^5$, qea.
