FLINT3.7.0-dev
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arb_hypgeom_ci

Synopsis#include <flint/arb_hypgeom.h>
void arb_hypgeom_ci(arb_t res, const arb_t z, slong prec)source

Sets res to the cosine integral \operatorname{Ci}(z) = -\int_z^\infty \cos(t)/t \, dt for z > 0. The result is indeterminate unless z is positive, since the value is complex for z < 0.

Implemented for real arguments with the same two methods as arb_hypgeom_si, using \operatorname{Ci}(z) = \gamma + \log z - \frac{z^2}{4}\, {}_2F_3(1, 1; 2, 2, \tfrac32; -z^2/4) for the convergent series.

Cite this page

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