Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 2 / 13D / e / Solution

At every lattice point $\omega =m{\omega }_1+n{\omega }_2$, the translated summand supplies a principal partAll other terms are holomorphic nearby. Hence the Weierstrass elliptic function has a double pole at every lattice point, with zero residue, and no other singularities.