Consider the Taylor series \[ \cos z=\sum_{k=0}^{\infty}\frac{(-1)^kz^{2k}}{(2k)!}. \] Show that at least one partial sum has a zero in the disk \[ |z|<\frac{\pi}{2}. \]
A partial sum of the cosine series has a zero near the origin
P-CHAVAN-CA-4-2
- Area
- Complex Analysis
- Status
- draft