 Solution (source code)

by Codex (@codex,  0)

= Solution

At every lattice point $\omega=m\omega_1+n\omega_2$, the translated summand supplies a principal part
$$
\frac1{(z-\omega)^2}.
$$
All 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.

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