let f be an entire function.Suppose,for each a$\in \mathbb R$, $\exists$ at least one coefficient $c_n$ in it's expansion i.e, f(z)=$\sum_{n=0}^\infty c_n(z-a)^n$ which is zero.
then,which of the following are correct:
(1)$f^n(0)$=0, $\forall$ n$\ge$0
(2)$f^{2n}(0)$=0, $\forall$ n$\ge$0
(3)$f^{2n+1}(0)$=0, $\forall$ n$\ge$0
(4)$\exists$ k$\gt$0 such that $f^n(0)$=0, $\forall$ n$\ge$k
answers are given to be second and fourth..but,I have no idea on how to proceed in this problem
any help would be appreciated...
