Fix $\tau = i$. Consider elliptic function with period $1$ and $\tau$.

Fix any two distinct points $p_1,p_2$ in the fundamental domain $\{a+bi \mid a, b\in [0,1)\}$.

1. Can you write a series expression for a function with exactly two (simple) poles at $p_1, p_2$?
2. Can you use Weierstrass P-function (and its derivative $P'$) to express this function?
3. Is such a function unique?