Let \(f\) be an entire function with the property that for all \(z\in \mathbb {C}\) there is \(n\) such that the \(n\)-th derivative \(f^{(n)}(z)=0\). Show that \(f\) is a polynomial.
Question
Math 6220 • Complex Analysis
Fall 2022 • Question 6
Question
Fall 2022 • Question 6
Let \(f\) be an entire function with the property that for all \(z\in \mathbb {C}\) there is \(n\) such that the \(n\)-th derivative \(f^{(n)}(z)=0\). Show that \(f\) is a polynomial.