acb_hypgeom_ei_asymp, acb_hypgeom_ei_2f2, acb_hypgeom_ei
Synopsis
#include <flint/acb_hypgeom.h>Sets res to the exponential integral \operatorname{Ei}(z), computed respectively from
\operatorname{Ei}(z) = -e^z U(1,1,-z) - \log(-z)
+ \frac{1}{2} \left(\log(z) - \log\left(\frac{1}{z}\right) \right),
\operatorname{Ei}(z) = z\, {}_2F_2(1, 1; 2, 2; z) + \gamma
+ \frac{1}{2} \left(\log(z) - \log\left(\frac{1}{z}\right) \right),
or by an automatic choice based on the expected accuracy of the two methods. The result is indeterminate if z contains zero.
Cite this page
The FLINT team, “acb_hypgeom_ei_asymp, acb_hypgeom_ei_2f2, acb_hypgeom_ei (acb_hypgeom.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/acb_hypgeom/acb_hypgeom_ei_asymp.html (generated 2026-10-20).
@misc{flint-doc-acb-hypgeom-acb-hypgeom-ei-asymp,
author = {{The FLINT team}},
title = {{acb\_hypgeom\_ei\_asymp, acb\_hypgeom\_ei\_2f2, acb\_hypgeom\_ei (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_ei_asymp.html},
note = {Generated 2026-10-20}
}