`acb_hypgeom_fresnel`

Synopsis#include <flint/acb_hypgeom.h>

void acb_hypgeom_fresnel(acb_t res1, acb_t res2, const acb_t z, int normalized, slong prec)source

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 2026-11-02).

@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 2026-11-02}
}

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