= Weierstrass quarter-period derivative identity
{c}
{title2=$\frac{\wp'(z-h_i)}{\wp'(z)}=-\frac{(\wp(h_i/2)-e_i)^2}{(\wp(z)-e_i)^2}$}
At $z=h_i/2$, evenness and periodicity give $\wp(z+h_i)=\wp(z)$. The <Weierstrass half-period translation formula> therefore identifies $(\wp(h_i/2)-e_i)^2$ with $(e_i-e_j)(e_i-e_l)$. Differentiating the <Weierstrass half-period translation formula> proves the identity, interpreted as equality of <meromorphic functions>, including the apparent singularities of its quotients.
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