FLINT3.7.0-dev
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acb_hypgeom_erf

Synopsis#include <flint/acb_hypgeom.h>
void acb_hypgeom_erf(acb_t res, const acb_t z, slong prec)source

Sets res to the error function erf⁡(z)=2π∫0ze−t2dt\operatorname{erf}(z) = \frac{2}{\sqrt\pi} \int_0^z e^{-t^2} dt.

Real input is passed to arb_hypgeom_erf. Otherwise the function uses the asymptotic expansion when its error term is below 2−prec2^{-\mathit{prec}} (with a reduced precision for the UU term), and otherwise the 1F1{}_1F_1 series better suited to the direction of zz, at a working precision increased by the 2min⁡(x2,y2)/log⁡22 \min(x^2, y^2)/\log 2 bits (for z=x+yiz = x + yi) lost to cancellation. For inexact zz the series is evaluated at the midpoint and the propagated error is bounded with acb_hypgeom_erf_propagated_error.

Cite this page

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