acb_hypgeom_ci_asymp, acb_hypgeom_ci_2f3, acb_hypgeom_ci
Synopsis
#include <flint/acb_hypgeom.h>Sets res to the cosine integral \operatorname{Ci}(z), computed respectively from
\operatorname{Ci}(z) = \log(z) - \frac{1}{2} \left[
e^{iz} U(1,1,-iz) + e^{-iz} U(1,1,iz) +
\log(-iz) + \log(iz) \right],
\operatorname{Ci}(z) = -\tfrac{z^2}{4}\,
{}_2F_3(1, 1; 2, 2, \tfrac{3}{2}; -\tfrac{z^2}{4})
+ \log(z) + \gamma,
or by an automatic choice. Positive real input is passed to arb_hypgeom_ci.
Cite this page
The FLINT team, “acb_hypgeom_ci_asymp, acb_hypgeom_ci_2f3, acb_hypgeom_ci (acb_hypgeom.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/acb_hypgeom/acb_hypgeom_ci_asymp.html (generated 2026-10-20).
@misc{flint-doc-acb-hypgeom-acb-hypgeom-ci-asymp,
author = {{The FLINT team}},
title = {{acb\_hypgeom\_ci\_asymp, acb\_hypgeom\_ci\_2f3, acb\_hypgeom\_ci (acb\_hypgeom.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/acb_hypgeom/acb_hypgeom_ci_asymp.html},
note = {Generated 2026-10-20}
}