acb_hypgeom_fresnel
Synopsis
#include <flint/acb_hypgeom.h>Sets res1 to the Fresnel sine integral S(z) and res2 to the Fresnel cosine integral C(z); either output may be NULL. If normalized is 0, S(z) = \int_0^z \sin(t^2) dt and C(z) = \int_0^z \cos(t^2) dt; if normalized is 1, the integrands are \sin(\tfrac12 \pi t^2) and \cos(\tfrac12 \pi t^2), the convention of Abramowitz and Stegun and of the DLMF. The values are computed from \operatorname{erf}((1 \pm i) w), where w is z times a real constant, evaluated at the midpoint of z with a bound for the propagated error.
Cite this page
The FLINT team, “acb_hypgeom_fresnel (acb_hypgeom.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/acb_hypgeom/acb_hypgeom_fresnel.html (generated 2026-10-20).
@misc{flint-doc-acb-hypgeom-acb-hypgeom-fresnel,
author = {{The FLINT team}},
title = {{acb\_hypgeom\_fresnel (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_fresnel.html},
note = {Generated 2026-10-20}
}