FLINT3.7.0-dev
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acb_elliptic_p

Synopsis#include <flint/acb_elliptic.h>
void acb_elliptic_p(acb_t r, const acb_t z, const acb_t tau, slong prec)source

Sets r to the Weierstrass elliptic function ℘(z,τ)=z−2+∑ω∈Λ∖0((z+ω)−2−ω−2)\wp(z, \tau) = z^{-2} + \sum_{\omega \in \Lambda \setminus 0} ((z + \omega)^{-2} - \omega^{-2}), computed by

℘(z,τ)=π2θ22(0,τ)θ32(0,τ)θ42(z,τ)θ12(z,τ)−π23[θ24(0,τ)+θ34(0,τ)].\wp(z, \tau) = \pi^2 \theta_2^2(0,\tau) \theta_3^2(0,\tau) \frac{\theta_4^2(z,\tau)}{\theta_1^2(z,\tau)} - \frac{\pi^2}{3} \left[ \theta_2^4(0,\tau) + \theta_3^4(0,\tau)\right].
Cite this page

The FLINT team, “acb_elliptic_p (acb_elliptic.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/acb_elliptic/acb_elliptic_p.html (generated 2026-11-02).