Let $f$ be a power series and $z$ a complex number such that $\hat{f}(|z|) < \infty$. Show then that the series $f$ converges at $z$ and that $|f(z)| \leqslant \hat{f}(|z|)$. Give an example where this inequality is strict.
Let $f$ be a power series and $z$ a complex number such that $\hat{f}(|z|) < \infty$. Show then that the series $f$ converges at $z$ and that $|f(z)| \leqslant \hat{f}(|z|)$. Give an example where this inequality is strict.