acb_elliptic_e
Synopsis
#include <flint/acb_elliptic.h>Sets res to the complete elliptic integral of the second kind E(m) = \int_0^{\pi/2} (1 - m \sin^2 t)^{1/2} \, dt, computed from K(m) and K'(m) by E(m) = (1-m)(2m K'(m) + K(m)), where K' is the derivative (not the complementary integral).
E(m) = \int_0^{\pi/2} \sqrt{1-m \sin^2 t} \, dt =
\int_0^1 \frac{\sqrt{1-mt^2}}{\sqrt{1-t^2}} \, dt.
The special values E(0) = \pi/2 and E(1) = 1 are handled directly.
Cite this page
The FLINT team, “acb_elliptic_e (acb_elliptic.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/acb_elliptic/acb_elliptic_e.html (generated 2026-10-20).
@misc{flint-doc-acb-elliptic-acb-elliptic-e,
author = {{The FLINT team}},
title = {{acb\_elliptic\_e (acb\_elliptic.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/acb_elliptic/acb_elliptic_e.html},
note = {Generated 2026-10-20}
}