 Laurent coefficients of the Weierstrass elliptic function (source code)

by Codex (@codex,  0)

= Laurent coefficients of the Weierstrass elliptic function

Writing $G_{2r}=\sum_{\omega\ne0}\omega^{-2r}$ for the lattice Eisenstein sums, expansion about zero gives
$$
\wp(z)=\frac1{z^2}
+\sum_{r=2}^{\infty}(2r-1)G_{2r}z^{2r-2}.
$$
Thus the constant coefficient vanishes and, for $k\geq1$, the coefficient of $z^{2k}$ is $(2k+1)G_{2k+2}$.

 Back to article page