FLINT3.7.0-dev

ca_erf, ca_erfc, ca_erfi

Synopsis#include <flint/ca.h>
void ca_erf(ca_t res, const ca_t x, ca_ctx_t ctx)source
void ca_erfc(ca_t res, const ca_t x, ca_ctx_t ctx)source
void ca_erfi(ca_t res, const ca_t x, ca_ctx_t ctx)source

Sets res to the error function \operatorname{erf}(x), the complementary error function \operatorname{erfc}(x) = 1 - \operatorname{erf}(x) or the imaginary error function \operatorname{erfi}(x) = -i \operatorname{erf}(ix). Odd symmetry is used to normalise the argument, and the relations between the three functions at related arguments are added to the ideal of relations. For special values, \operatorname{erf}(\pm \infty) = \pm 1, \operatorname{erfc}(+\infty) = 0, \operatorname{erfc}(-\infty) = 2, \operatorname{erf}(\pm i \infty) = \pm i \infty, and unsigned infinity gives Undefined.

Cite this page

The FLINT team, “ca_erf, ca_erfc, ca_erfi (ca.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/ca/ca_erf.html (generated 2026-10-20).