FLINT3.7.0-dev
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acb_asin, acb_acos, acb_atan

Synopsis#include <flint/acb.h>
void acb_asin(acb_t r, const acb_t z, slong prec)source
void acb_acos(acb_t r, const acb_t z, slong prec)source
void acb_atan(acb_t r, const acb_t z, slong prec)source

Set r to asin⁡z=−ilog⁡(iz+1−z2)\operatorname{asin} z = -i \log(iz + \sqrt{1 - z^2}), acos⁡z=π/2−asin⁡z\operatorname{acos} z = \pi/2 - \operatorname{asin} z, respectively atan⁡z=i2(log⁡(1−iz)−log⁡(1+iz))\operatorname{atan} z = \tfrac{i}{2} (\log(1 - iz) - \log(1 + iz)). The branch cuts are (−∞,−1)∪(1,∞)(-\infty, -1) \cup (1, \infty) for asin⁡\operatorname{asin} and acos⁡\operatorname{acos}, and (−i∞,−i)∪(i,i∞)(-i\infty, -i) \cup (i, i\infty) for atan⁡\operatorname{atan}.

Cite this page

The FLINT team, “acb_asin, acb_acos, acb_atan (acb.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/acb/acb_asin.html (generated 2026-11-02).