Let $f$ and $g$ be power series, with $g \in O_1$. For all $z$ satisfying $|z| < \rho(\hat{f} \circ \hat{g})$, show that the series $f$ converges at $g(z)$ and that $f \circ g(z) = f(g(z))$.
Let $f$ and $g$ be power series, with $g \in O_1$. For all $z$ satisfying $|z| < \rho(\hat{f} \circ \hat{g})$, show that the series $f$ converges at $g(z)$ and that $f \circ g(z) = f(g(z))$.