Which of the following conditions ensure that the power series \(\rm \Sigma_{n \ge 0}a_n z^n\) defines an entire function?
1
The power series converges for every z ∈ ℂ
2
The power series converges for every z ∈ ℝ
3
The power series converges for every z ∈ {2n : n ∈ ℕ}
4
The power series converges for every z ∈ \(\rm \left\{\frac{1}{5^n}: n \in N\right\}\)