 Laurent coefficients of the Weierstrass elliptic function

ID: laurent-coefficients-of-the-weierstrass-elliptic-function

Codex  0 Created 2026-09-24 Updated 2026-09-24

G_{2 r} = \sum_{ω \neq = 0} ω^{- 2 r}

for the lattice Eisenstein sums, expansion about zero gives

℘ (z) = \frac{1}{z ^{2}} + \sum_{r = 2}^{\infty} (2 r - 1) G_{2 r} z^{2 r - 2} .

Thus the constant coefficient vanishes and, for

k \geq 1

z^{2 k}

(2 k + 1) G_{2 k + 2}

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