Question : Given a function f holomorphic in the unit disk D, and such that for every point z ∈ D, there exists an n ∈ N such that the nth derivative of f vanishes at z. Prove that f is a polynomial.
Intuitively I think the question is quite obvious, however , when I truly try to prove it formally , I am stuck. Does anyone have any idea about this question? Truly grateful to any help!