Suppose f is an analytic function defined everyWhere in C and such that for each z₀ ∈ C at least one coefficient in the expansion [infinity] f(z) = ∑ cₙ(z - z₀ ) ⁿis equal to 0 . Prove ​ ⁿ ⁼ ⁰ that f is a polynomial. [Hint: Use the fact that cₙn! = fⁿ(z₀) and use a countability argument. ]
​ is equal to 0 . Prove that f is a polynomial. [Hint: Use the fact that cₙn! = fⁿ(z₀) and use a countability argument. ]