Let \(f\) be an entire function such that \(f'=f\). Show that \[ f(z)=f(0)e^z=f(0)\sum _{n=0}^{\infty }\frac {z^n}{n!} \] for any \(z\in \mathbb C\).
Question
Math 6210 • Real Analysis
2004 • Question 6
Question
2004 • Question 6
Let \(f\) be an entire function such that \(f'=f\). Show that \[ f(z)=f(0)e^z=f(0)\sum _{n=0}^{\infty }\frac {z^n}{n!} \] for any \(z\in \mathbb C\).