acb_elliptic_e_inc
Synopsis
#include <flint/acb_elliptic.h>Sets res to the incomplete elliptic integral of the second kind E(\phi, m) = \int_0^\phi (1 - m \sin^2 t)^{1/2} \, dt, extended by E(\phi + d\pi, m) = 2 d E(m) + E(\phi, m). With times_pi nonzero, \phi is replaced by \pi \phi. In particular E(\pi/2, m) = E(m).
E(\phi,m) = \int_0^{\phi} \sqrt{1-m \sin^2 t} \, dt =
\int_0^{\sin \phi}
\frac{\sqrt{1-mt^2}}{\sqrt{1-t^2}} \, dt.
Cite this page
The FLINT team, “acb_elliptic_e_inc (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_inc.html (generated 2026-10-20).
@misc{flint-doc-acb-elliptic-acb-elliptic-e-inc,
author = {{The FLINT team}},
title = {{acb\_elliptic\_e\_inc (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_inc.html},
note = {Generated 2026-10-20}
}