grandes-ecoles 2018 Q34

grandes-ecoles · France · centrale-maths2__official Taylor series Prove smoothness or power series expandability of a function

Let $f$ be a function that expands as a power series on $D(0,R)$. Show that $\forall r \in [0, R[$, $|f(0)| \leqslant \sup_{t \in \mathbb{R}} |f(r\cos(t), r\sin(t))|$.

Let $f$ be a function that expands as a power series on $D(0,R)$. Show that $\forall r \in [0, R[$, $|f(0)| \leqslant \sup_{t \in \mathbb{R}} |f(r\cos(t), r\sin(t))|$.

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